REESE  LIBRARY 


UNIVERSITY  OF  CALIFORNIA. 


ASTRONOMY 
'/<<vt'rm/        LIBRARY 

•essioi  786     .   Class  No. 


r- u— u— iP 


v^rt* 


/ 


I 


V 


TABLES  OF  YICTOEIA. 


lf;  '•  :  ~J   •      *  '' 


TABLES 


OF 


VICTORIA 


COMPUTED  WITH  REGARD  TO  THE 


at 


- 

BY 

P.  BRtJNNOW.  PH.  DR. 

»«  7 

PBOFESSOB  OF  ASTKONOM?  IN  THE  UNIVERSITY  OF  MICHIGAN,  AND  DIKECTOB 
OF  THE  OBSEBVATOJBY  AT  ANN  ARBOE. 


&8  ©rtiet  of  JJoart)  of 
»-»« 


NEW     YORK: 
B.    WESTERMANN    AND    COMPANY. 

LONDON:  N.  TRUBNER  AND  COMPANY. 
M.DCCC.LIX. 


ASTRONOM^ 
LIBRARY 


GEORGE    H.     FLEMING, 
Book  Printer,  Detroit,  Michigan,  U.  S.  A. 


i 


N  No.  1077  of  the  Astronomische  Nachrichten  I  have  published  the  expressions 
of  the   perturbations   of  Victoria,   produced   by  Jupiter   and   Saturn,  together 
with   the   elliptical   elements  as   they  were   derived   from  the  five  oppositions   of 
the  planet,  in  1850,  1852,  1853,  1854,  and  1856.      Since  then  I  have  published, 
in  No.  108  of  the  Astronomical  Journal,  the  corrections  which  these  elements  re- 
quired according  to  the   observations  at  the  time  of  the  last  opposition  in  1857. 
As   these   corrections   are  very  small,  I  consider  now  the  elliptical  elements,  and 
especially  the  mean  motion  of  the  planet,  as  so  nearly  known  that  they  will  give, 
even  for  a  considerably  distant  time,  the  place  of  the  planet  with  great  approx- 
imation.    I  therefore  have  not  delayed  the  construction  of  tables  any  longer.     The 
computations  which  I  have  made  for  this  Asteroid  since  the  time  of  its  discovery 
have  thus  been  brought  to  a  close;     and  I  feel  happy  to  have  contributed  this 
mite  to  the  advancement  of  a  branch  of  Astronomy  which  will  require  the  judi- 
cious co-operation  of  all  Astronomers,  in  order  to  master  the  constantly  increasing 

material. 

I  hope,  then,  that  Astronomers  will  accept  these  Tables  with  indulgence,  and 

appreciate,  at  least,  the  good  intention  of  the  Author. 

The  perturbations  were  calculated  from  the  formulae  published  by  Professor 
HANSEN,  in  No.  799  of  the  Astronomische  NacJirichten  —  formulae  which  were  de- 
veloped and  integrated  by  the  methods  used  for  the  calculation  of  the  perturb- 
ations of  Flora.  The  Tables  give,  therefore,  the  Perturbations  of  the  Mean 
Anomaly,  those  of  the  Logarithm  of  the  Elliptical  Radius  Vector  (computed 

74786 


itself  with  the  corrected  mean  anomaly),  and  those  of  the  Co-ordinate  £  vertical 
to  the  elliptical  orbit,  or  rather  the  corrections  of  the  three  Co-ordinates  of  the 
Planet  with  respect  to  the  plane  of  the  Equator  and  the  line  of  the  Equinoxes, 
owing  to  the  Perturbations  g. 

As  to  the  expressions  of  the  perturbations,  I  refer  to  the  Astronomishe 
Nachrichten,  No.  1077.  If  M.  denotes  the  mean  anomaly  of  Victoria,  it  that 
of  Jupiter,  and  ^  that  of  Saturn,  the  arguments  of  the  different  tables  are  as 
follows : 

1.  M  —  2£  20.     4M  —  5  It 

2.  M  —  22£  21.     2M  —  3*? 

3.  2M  —  32£  22.     52£—  M 

4.  2£  23.     3M  —  2£ 

5.  M  —  32£  24.       M  +  22£ 

6.  42£—  M  25.  4M  —  32£ 

7.  72£  —  2M  26.  M  +  32£ 

8.  2M  —  52£  27.  4M— 72£ 

9.  3M— 42£  28.  6%.  —  M 

10.  M  29.     2M  +  2£ 

11.  3M  —  22£  30.     3M  — 82£ 

12.  3M  —  52f  31.     5M—  62f 

13.  3M  —  72f  32.     5M  —  42^ 

14.  M-2^  33.     72f— M 

15.  2M—  2f  34.     5M  — 72^ 

16.  M— T>  35.     5M  — 82f 

17.  i>  36.     2M—  ^ 

18.  M+ 2f  37.     3M  — 2^ 

19.  M— 3^ 

The  elliptical  elements  which  have  been  used  in  the  construction  of  the 
Tables  are  as  follows: 

1851,  Jan.  o.o.     WASHINGTON  MEAN  TIME. 

Mean  Anomaly 66°  6'  49^.79 

Longitude  of  Perihelion 301  39  25  .02  )  Referred  to  the  Mean  Equinox 

Longitude  of  Ascending  Node ....  235  34  41  .74  j       of  1851,  Jan.  o. 

Inclination 823    1 7  .74 

Angle  of  Excentricity 1238  44  .90 

Mean  Daily  Motion 994*.8347237 

Logarithm  of  half  Great  Axis   ...       0.3681389 


Though    the   Tables   need   no   further   explanation,   I   will   give    here,   as   an 
example,    the  computation  of  the  heliocentric    co-ordinates   of  Victoria   for   1857 

August 

13.5,  Washington   Mean   Time. 

We 

must   form 

first   the 

different 

Arguments   from 

Table   I. 

i. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

1857 

Aug. 

13 

12  hours 

311.071 
40.972 

2-513 
96 

310.283 
23.357 
!-433 
55 

261.355 
64.328 
3-944 
151 

0.786 
17.613 
1.080 
42 

309-497 

5-744 
0.352 
13 

51.29 
11.87 
0-73 

2 

101.79 
6.13 
0.38 
i 

259.78 
29.10 

1.78 

7 

354.652 

335-I28 

329-778 

19.521 

315.606 

63.91 

108.31 

290.73 

9. 

10. 

11. 

12. 

13. 

14. 

15. 

16. 

1857 
Aug. 

13 
12  hours 

212.42 
105.30 
6.46 
25 

311.858 
58.585 
3-592 
138 

H-I73 

213.99 

1  40.5  3 
8.62 

33 

211.64 
87.69 
5.38 

20 

210.06 
52.46 
3.21 

12 

292.81 
44.40 
2.72 
ii 

262.92 

99.56 
6.1  1 

24 

302.33 
51.49 
3.16 

12 

32443 

347 

304-91 

265.85 

340.04 

8-83 

357-10 

17. 

18. 

19. 

20. 

21. 

22. 

23. 

24. 

1857 
Aug. 

*3 
12  hours 

9.52 
7.09 
0.44 
i 

312.6 

76.1 
4-7 

2 

283-3 
37-3 
2.3 
i 

163.5 
H6.3 
9.0 

4 

235-1 
95-9 

5-8 

2 

52.1 
29.5 
1.8 

214.8 
158.1 
9-6 

4 

3I3.4 
93-8 

5-7 

2 

17.06 

33-6 

323-0 

319.2 

337-0 

834 

22.9 

53-1 

25. 

26. 

27. 

28. 

29. 

30. 

31. 

32. 

1857 
Aug. 

13 
12  hours 

165.1 
181.5 
ii.  i 

5 

314.2 
111.4 
6.8 

2 

161.9 

III.O 

6.8 

2 

52.8 
47.1 
2.9 
i 

264.5 
134.8 

8.2 
2 

209.3 
34-9 

2.1 

I 

1  14.6 

I8/-3 
11.5 

5 

1  16.2 
222.5 
13.6 
5 

358.2 

72.6 

279.9 

102.9 

47-7 

246.4 

3*3-9 

352.8 

- 

33. 

34. 

35. 

36. 

37. 

1857 
Aug. 

'3 

1  2  hours 

53.6 
64.7 
4.0 
i 

113.8 
169.6 
10.4 

4 

113.0 
152.0 
9.2 

4 

254.1 

I  I  O.I 

6.8 

2 

196.6 
161.6 

9-9 

4 

' 

122.4 

294.2 

274.6 

II.  2 

8-5 

6 
With   these    Arguments   we   find,    then,    the   following   perturbations: 


Arg. 

2.     335-128 
3.     329.778 
4.       19.521 
5.     315.606 
6.       63.91 
7.     108.31 
8.     290.73 
9-     324-43 

10.     14.173 

11-         3-47 
12.     304.91 
13.     265.85 
14.     340.04 
15.         8.83 
16.     357.10 
17.       17.06 
18.       33-6 
19.     323.0 
20.     319.2 
21.     337.0 
22.       83.4 
23.       22.9 

24.       53.1 
25.     358.2 

26.       72.6 
27.     279.9 
28.     102.9 
29.       47.7 
30.     246.4 

31-     3»3.9 
32.     352.8 
33.     122.4 
34.     294.2 
35.     274.6 
36.       1  1.  2 
37.         8.5 

Terms  mult,  by  t 
Perturbations 

SM. 

249.71 
318.27 
0.17 
60.71 
162.29 
0.97 
5.69 
7.62 
1  1.  06 
18.14 

3-44 
o-37 
7-31 
16.31 
11.87 

9-39 

1.23 

2.45 
4.28 
2.79 
2.04 
1.46 
1.36 
1.24 
0.14 

°-93 
0.26 
0.03 
0.15 

O.I  I 

0.8  1 

0.70 
0.19 

0.62 
0.27 
0.31 
0.47 

$  Tog.  r. 

4336- 
3932 
3052 
500 
1932 
166 

64 
188 

405 
18 
411 
140 
179 

21 

224 
19 

6 

92 
6 
40 
7 
25 
29 
36 
36 

17 

3 
10 

17 

2 
10 

9 
o 
6 
i 

4 

279.9 
268.5 
69.6 

25-1 

70.5 

0.2 
1.0 

9-9 
25.1 

3-3 
2-3 
5.6 
11.4 

3-2 

36.9 
1.9 

46.8 

0.8 

1.2 

0.0 
2-5 

4.6 

O.I 

o-3 
4-4 

4-3 
6.1 

M.                                        t. 

1857         311     23        1.22                                    +6.OOI 

Aug.        58  35     4.96                                580 
13  days        3  35   32.85                                 35 
12  hours             8   17.4-2                                       i 

M0           13  41    56.45                           +6.617 
SM                  13  38.40 

M            13  55   34.85 
Eq.  ofC.  +8     8  59.53   from  Table  XII. 

v         22     4  34.38 
log.  r0        0.2655504    from  Table  XIII. 
5  log.  r                 !54°9 

log.  r          0.2670913 

Then  one  takes  A,  B,  C,  log.  «, 
log.  bj  and  log.  c  from  Table  XIV., 
and  finds: 

A  +  v       53  31  45.58 
IB  +  v     321   ii   38.29 
C  +  v     343     6  53.06 

ar              0.2639174 
sin  (A  +  v)      9.9053431 

Or       0.2438883 
sin  (JB  +  v)    9.797049971 

cr         9.7990453 
sin  (C  +  v)   9.4630805^ 

X0       +1.4765918 
Corr.  +169  from  Table  XV. 

y0      -1.0988493 
Corr.                 +448  from  Table  XV. 

20         —0.1828630 

Corr.                 -1322  from  Table  XV. 

905.16 
—  13.11  1 

15974 

-85.45 
=  +6.617 

892.3 
—  2.76 

The  heliocentric  co-ordinates,  re- 
ferred to  the  equator  and  the  mean 
equinox  of  1857.0,  are,   therefore: 

x  =  +1.4766087 
y  =  —  1.0988045 
z  —  —0.1829952 

-   86.76 
818.40 

565 
15409 

-18.3 
874.0 

If  one  wishes  to  calculate  only  an  approximate  place,  it  will  be  sufficient  to 
take  into  account  only  the  first  five  equations  in  »M.,  *Log.r,  and  {,  together, 
with  the  Terms  multiplied  in  t     In  this  case,  one-must  take  M.  and  Log.r0 
Table  XVII,  and  corrections  of  the  three  co-ordinates  a,  y,  2,  from  Table  XVI. 


TA.BLES. 


TABLE 

Arguments  for  the  Perturbations 

(Referred  to  the  Meridian 

Year. 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

1850 

176.906 

28.564 

205.470 

148.342 

240.221 

268.12 

27.90 

268.79 

22.37 

325-249 

319.06 

234.03 

1851 

247.446 

68.778 

316.224 

178.667 

250.1  10 

288.55 

38.45 

318.89 

203.66 

66.1  14 

2OI.OO 

25.00 

18525 

318.179 

109.102 

67.281 

209.076 

260.025 

309.05 

49-03 

9-'  3 

25-45 

167^55 

83.61 

176.38 

1853 

28.718 

1  49-3*7 

178.035 

239.401 

269.914 

32949 

59-57 

59-24 

206.75 

268.120 

325.56 

327.35 

1854 

99.258 

189.530 

288.789 

269.727 

279.803 

349.92 

70.12 

109.34 

28.04 

8.985 

207.50 

118.32 

1855 

169.798 

229.745 

39-544 

300.052 

289.692 

10.35 

80.67 

159-44 

209.33 

109.851 

89.45 

269.29 

1856.6 

240.531 

270.069 

150.601 

330.461 

299.608 

30.85 

91.24 

209.68 

31.12 

210.992 

332.05 

60.67 

1857 

311.071 

310.283 

261.355 

0.786 

309-497 

51.29 

101.79 

25978 

212.42 

311.858 

213.99 

21  1.64 

1858 

2  1  .6  1  0 

350.498 

12.109 

3I.I  12 

319.386 

71.72 

112.34 

309.89 

33-7' 

52-723 

95-94 

2.6  I 

1859 

92.150 

30.712 

122.863 

61.438 

329.275 

92.16 

122.88 

359-99 

2  I  5  .0  I 

153.588 

337.89 

'53-57 

1860.8 

162.883 

71.036 

233-9'9 

91.847 

339-'89 

112.66 

133.47 

50.23 

36.80 

254-730 

220.49 

304.95 

1861 

233.423 

1  11.250 

344-673 

122.172 

349.078 

133-10 

144.02 

100.33 

218.09 

355-595 

102.43 

95.92 

1862 

303-963 

151.465 

95427 

152.498 

358-967 

'53-53 

154.56 

15044 

39-39 

96.460 

344-38 

246.89 

1863 

14.502 

191.679 

206.181 

182.823 

8.856 

'73-97 

165.11 

200.54 

220.68 

197.326 

226.32 

37-86 

18645 

85-235 

232.004 

317-239 

213.232 

18.772 

194.46 

175.69 

250.78 

42-47 

298.467 

108.93 

189.24 

1865 

'55-775 

272.218 

67.994 

243-557 

28.661 

214.90 

186.23 

300.88 

223.77 

39.332 

350.88 

340.21 

1866 

226.315 

312.433 

178.748 

273.883 

38.55° 

235-34 

196.78 

350-99 

45.06 

140.197 

232.82 

131.18 

1867 

296.855 

352.647 

289.502 

304.209 

48.439 

255-77 

207.33 

41.09 

226.35 

241.063 

114.77 

282.15 

18685 

7-588 

32.972 

40.560 

334.6I7 

58.355 

276.27 

217.90 

9L33 

48-15 

342.204 

357.38 

73-53 

1869 

78.128 

73.186 

'5'-3'4 

4.942 

68.244 

296.70 

228.45 

'  4'  -43 

229.44 

83.069 

239.32 

224.50 

1870 

148.667 

113.401 

262.067 

35.267 

78.133 

3'7-'3 

239.00 

I9I-53 

5073 

183-934 

121.27 

'5-47 

1871 

219.207 

153.616 

12.822 

65.592 

88.023 

337-57 

249.55 

241.63 

232.02 

284-799 

3-2' 

166.44 

18725 

289.940 

193.940 

123.880 

96.OOO 

97.940' 

358.06 

260.12 

291.88 

53-82 

25.940 

245.82 

317-82 

1873 

0.480 

234-I55 

234-635 

126.326 

107.829 

18.49 

270.67 

341.98 

235.11 

126.806 

127.76 

108.79 

1874 

71.020 

274.370 

345-39° 

156.651 

117.719 

38.93 

281.21 

•  32.08 

56.41 

227.671 

9.71 

259.76 

1875 

141.560 

3H-584 

96.145 

186.976 

127.608 

59.36 

291.76 

82.19 

237.70 

328.536 

251.65 

50.73 

18765 

212.294 

354-9°9 

207.203 

217.384 

137-525 

79.86 

302.33 

'32-43 

59-49 

69.678 

134.26 

2O2.  12 

1877 

282.834 

35-124 

317.958 

247709 

'47-4'  5 

100.29 

312.88 

182.53 

240.79 

I70.543 

1  6.2  I 

353.09 

187-8 

353-374 

•'75-339 

68.713 

278.034 

157.304 

120.73 

323-42 

232.64 

62.08 

271.408 

258.15 

I  44.06 

1879 

63-9  '4 

'15-554 

179.467 

308.360 

167.194 

141.16 

333-97 

282.74 

243-38 

12.273 

140.10 

295.03 

i88o5 

134.647 

I55-879 

290.526 

338.768 

177.111 

161.66 

344-55 

332.99 

65-17 

"34'5 

22.71 

86.40 

1881 

205.187 

196.094 

41.281 

9-°93 

187.001 

182.09 

355-10 

23-09 

246.46 

214.280 

264.65 

237.37 

1882 

275.727 

236.309 

152.036 

39-418 

196.891 

202.53 

5.64 

73.20 

.  67.76 

3'5-'45 

146.60 

28.34 

1883 

346.267 

276.524 

262.791 

69743 

206.781 

222.96 

16.19 

123.30 

249.05 

56.011 

28.54 

'79-3' 

18845 

57.001 

316.849 

13.850 

100.152 

216.698 

243.46 

26.76 

'73-55 

70.85 

157.152 

271.15 

330.69 

1885 

127.541 

357.064 

124.605 

130.477 

226.588 

263.89 

37-3° 

223.65 

252.14 

258.017 

153.10 

121.66 

1886 

198.081 

37.279 

235.360 

160.802 

236.478 

284-33 

47-85 

273.76 

73-44 

358.882 

35-04 

272.63 

1887 

268.621 

77-494 

346.H5 

191.127 

246.368 

304.76 

58.39 

323.86 

254-73 

99.748 

276.99 

63.60 

18885 

339-354 

117.820 

97-174 

221.535 

256.285 

325-z5 

68.96 

14.10 

76.52 

200.889 

159.60 

214.98 

1889 

49.894 

158.035 

207.929 

251.860 

266.175 

345.69 

79-5  ' 

64.21 

257.82 

301-754 

41.54 

5-95 

1890 

120.435 

198.250 

318.684 

282.185 

276.065 

6.12 

90.05 

114.31 

79-12 

42.620 

283.49 

156.93 

1891 

190.975 

238.465 

69439 

312.510 

285.955 

26.55 

100.59 

164.41 

260.41 

143.485 

165.43 

307.90 

18925 

261.709 

278.791 

180.498 

342.918 

295.873 

47.05 

111.17 

2  I  4.66 

82.20 

244.627 

48.04 

99.28 

i«93 

332.249 

319.006 

291.254 

13.244 

305-763 

67.48 

121.71 

264.76 

263.49 

345-492 

289.99 

250.25 

1894 

42.789 

359.221 

42.009 

43-568 

3I5-653 

87.92 

132.26 

3I4.87 

84.79 

86-357 

'7'-93 

41.22 

1895 

113-33° 

39-436 

152.765 

73-894 

325-543 

108.35 

142.80 

4-97 

266.09 

187.222 

53-88 

192.19 

18965 

184.063 

79.762 

263.824 

104.302 

335-46i 

128.84 

'53-38 

55-21 

87.88 

288.364 

296.49 

343.58 

1897 

254.603 

119.977 

'4-579 

134.627 

345-351 

149.28 

163.92 

105.32 

269.18 

29.229 

17843 

'34-55 

1898 

325-I44 

160.192 

125-334 

164.951 

355-241 

169.71 

174-47 

155.42 

90.48 

1  30.094 

60.38 

285.52 

1899 

35.684 

200.407 

236.089 

195.276 

5-»3» 

190.15 

185.01 

205-53 

271.78 

230.959 

302.32 

76.49 

1900- 

106.223 

240.622 

346.845 

225.601 

15.021 

210.58 

195.56 

255.64 

93-07 

331.824 

184.27 

227.47 

I. 

for  the  Different  Years. 

of  Waftiington. 


MBWB^^H 

1  3 

t^a^mmmmf 

14. 

•HK^Knm 

15. 

«»B^K>K 

16. 

w*m 

i 

17. 

•••«•• 
18. 

«—  —  - 
19. 

mxmmmfs*^*' 

20. 

^mfwmmm^ 

21. 

«Bi«e» 

22. 

, 

23. 

•M^MB 

24. 

•^^•« 
25. 

,—  *« 

26. 

27. 

Year. 

i.  O. 

297-34 

27.66 

118.22 
208.54 
298.86 
29.18 
119.74 

210.06 

300.38 
30.70 
121.26 
211.58 

301.90 
32.21 

117.28 
193.72 

270.18 
346.^2 
63.27 

i  39-7  i 
216.37 
292.81 
9.26 
85.71 
162.37 
238.82 
315.26 
3I-7I 

142.15 
3I3.55 
12543 
296.83 
108.24 
279.64 

9I-52  , 

262.92  : 

74-3  3  j 
245-73 
57.60 
229.00 
40.41 
211.81 

41.26 

129.91 

2  1  8.8  1 

307.47 

36.12 

124.78 
213.68 
302.33 
30-99 

119.64 
208.54 
297.20 

25.85 
114.51 

283.99         H3.6 
296.2O        244.8 
308.44            l6.3 
320.65         H7.5 

;  332.86    278.7 

!  345-07      49-9 
1  357.31     181.4 
9.52    312.6 
21.73  !    83.8 
33-94    215.0 
'•'    46.18    346.6 
58.39    117-8 
70.60    249.0 

82.8l         20.2 

193-3 
257-5 
321.9 
26.2 
90.4 
154.6 
219.0 
283.3 
347-5 
5^-7 

I  1  6.  2 

180.4 
244.7 
308.9 

199-3 
91.1 

343-7 

235-5 
127.3 

19.1  j 
271.7 
163-5 
55-3 
307.2 

199.7 
91.5 
343-4 
235-2 

158.5 

323-6 
129.1 
294.2 

99-3 
264.4 
70.0 

235-1 
40.2 
205.3 
10.9 
176.0 

341-1 

146.2 

56.4   107.4 
107.2      19.7 
158.1    292.7 
208.8    205.0 
259.6    117.2 
3104      29.5 
1.3    302.5 
52.1    214.8 

102.9    ;     127.0 

153-7  !    39-3 
204.5    312.3 
255-3    224.6 
306.0    136.9 
356.8i    49.1 

261.9 
634 
2254 
26.9 
188.4 

349-9 
151.9 

3  '34 
114.9 
2764 
784 

239-9 
414 

203.0 

136.0 
88.5 
41.8 

354-3 
306.8  i 

259.3 

212.6 
165.1 
II7.6 

7O.I 
234 

335-9 
2884 

240.9 

T  r\  A  t 

50.3 
242.1 

74-5 
266.3 
98.2 
290.0 
122.4 

3H-2 
146.1 

337-9 
170.3 

2.1 

194.0 
25.8 
2l8.2 

262.6 

93-8 
285.5 
116.7 

307.9 
139.0 

330.7 
161.9 

353-1 
184.3 
1  6.0 

207.2 

38.4 
229.6 

6l    T, 

1850 
1851 
1852.6 

1853 
1854 
1855 
1856,5 
1857 
1858 
1859 
1860.5 
1861 
1862 
1863 
1864^8 

122.78 
213.10 
30342 

33.74 
124.30 

214.62 
304-94 

35-26 

125.83 

216.14 
306.46 

36.78 

127.35 
217.67 

3°7-99 
38.30 
128.87 
219.19 
309-51 
39.83 
130.40 
220.72 
311.04 
41.36 

i3'-93 
222.25 
312.56 
42.88 

133-45 
223.77 
3  '  4-°9 
44.41 

134.98 
225.30 
315.62 

45-95 

136.27 

108.37         23.68      203.41   : 
184.81       195.09      292.06 
261.26           6.50         20.72 

337-71     I77-9°    I09-37 
54.36    349.78     198.27  : 
130.81     161.19    286.93 
207.25     332.60      15.59 
283.69     144.01     104.24 
0.34    315.88     193.14 
76.79    127.29    281.79 
153.23    298.69       10.45 
229.67     1  10.  10      99.10 
306.32    281.97     188.00 
22.77      93-38    276.65 
99.21     264.79         5.31 
175.65  !     76-20      93.96 
2^2.31  i  248.06     182.86 
328.75  i    59-47    271.51 

45.19    ':    230.87               O.l6 
121.63    ;        42.28            88.82; 

i  198.28  ;  214.15     I77-71 
274.72  !    25.56    266.36 
351.16  i  196.97    355-01 
67.60        8.37      83.67 
144.25     180.25     172.56 
220.69  '351.65    261.21 
297.12    163.05    349.87 
i3-57i334-46      78.53 
90.23    146.33     l67-43 
166.68  :  317.74    256.08 
243.13     129.14    344-74 

3'9-57  i  300-55      73-4° 
36.23    112.42    162.30 
112.68:283.83    250.95 
189.13!    95.24    339.61 
265.58  i  266.65      68.27 
342.02      78.05     156.92 

95.05 
107.26 
119.47 
131.68 

H3-93 
156.14 

168.34! 
180.55  ' 
192.79 
205.00  , 
217.21 
229.42  ; 
241.67 
253.88 
266.09 
278.30 
290.55 
302.76 

3  1  4-97 
327-19 
339-43 

35««4 

3-86 
16.07 
28.32 
40.53 
52.75 
64.96 
77.20 
89.41 
101.62 

113-83 
126.07 
138.28 
150.48 
162.69 
174.90 

151.7      J3'3     I27-7 
282.9      77.5       19-5 
54.1     141.81271.4 
185.3    206.0    163.2 
316.8    270.4,    55.7 
88.0    334.6    307.6 
219.2  ;     38.9     199.4 
350.4     103.1        91.2 
121.9    167.5     343-8 
253.1  :  231.8    235.6 
24.3    296.0    127.4 
155.5  ;      0.2       19.2 
287.1  ;    64.6    271.8 
58.3    128.9    163.6 
1894    193.1      55-4 
320.6  i  257.3    307.3 
92.2  i  321.8    199.8 
223.4      26.0      91.6 
354.6      90.2    343.5 
125.8    154.4    235.3 
257.3    218.8    127.8 

28.5  :  283.1     19.6 

159-7    347-3    271.5 
290.9      51.5     163.3 
62.4    1  1  5.9      55-8 
193.6    180.1     307.7 
324.8    244.4    199.6 
96.0    308.6      91.4 
227.5  !    !3-°    344-o 
358.7      77.2    235.8 
129.9    141.5    127.6 
261.1  i  205.7      19.4 
32.7    270.1    272.0 

163.9    334-4    l63-8 
295.1      38.6      55.6 
66.3     102.8    307.5 
197.4    167.1     199.3 

3JI-7 
1  1  6.8 

281.9 
87.0 
252.6 

57-7 

222.8 
27.9 
193-4 
358.5 
163.6 

328.7 

134-3 
299.4 
104.5 
269.6 

75-2 
240.3 

45-4 
210.5 
1  6.0 
iBi.i 

346.2 

151-3 
316.8 
121.9 
287.0 
92.1 

257-6 
62.7 
227.8 

32.9 
198.5 

3-6 
168.7 

333-8 
138-9 

47-7 

98.5 
149.2 

2OO.O 
250.9 

3OI-7 
3524 
43-2 
94.1' 
144.8 
195.6 
246.3 
297.2 
348-o 
38.8 
89.5 

H04 
191.2 

241.9 
292.7 
343-6 

34-3 
85.1 

135-8 
186.7 

237-5 
288.3 

339-1 
30.0 

80.7 

131-5 
182.2 

233-' 
283.9 

334-7 

25-4 
76.2 

yt£.i          ^-.y     Lyt'" 
234.4    166.4    146.7 
146.7    328.0      99.2 

59-o   I29-5     51-? 
332.0  2914       5.0 

244.3     92.9   3  i  7-5 
156.5    254.5   269.9 
68.8      56.0  .  2224 
341.8    218.0    175.7 
254.1      19.5    128.2 
166.3    181.0     80.7 

78.6  :  342-5      33-2 
351.6    144.5    346-6 
263.9   3°6.o   299.0 
176.2    107.5   2Sl-S 

88.5   :  269.1    ,  204.0 

1.5     7°-9   1  5  74 
273.8   2324   109.9 

1  86.1  ;    33.9     624 
98-3  i  195-5      H-9 
11.3    3574  328.2 
283.6;  158.9   280.7 
195-9   320.5    233.2 

108.2     122.0     185.7 
21.2:283.9     139.0 
293.5        85.5!     91.5 
2057     247.0        43-9 

1  1  8.0  j    48.5    356.4 
31.01210.5  1309.7 

303.3  i      I2.O  j  262.2 
215.6     173.5     214.7 
127.8     335-0     167.2 

40.8  :  137.0  120.6 
313.11298.5    73.1 

2254,  100,0     25.5 

137.7  1  261.5  338.0 

49.9  !     63.0     290.5 

50.0  ; 
241.8 

73-6 
266.0 

97-8 
289.7 
121.5 
3!3-9 

1  45  -7 
337-5 
1694 

i-7 
193.6 

254 

217.2 

49-7 
,241.5 

734 
265.2 

97-6 
289.4 

I  2  1.  2 

3I3-° 
1  45  4 
337.2 
169.1 
0.9 

I93.3 
25.1 
216.9 
!  48.8 
241.1 

73-0 
264.8 
96.6 
288.5 

»»«j 

252.5 

837 
274-8 
1  06.6 

297-8 
129.0 
320.2 
151.9 
343-1 
174-3 

5-5 
197.2 

28.4 
219.6 
50.7 
242-5 
73-7 
264.9 
96.1 
287.8 
119.0 
310.2 
141.3 

333-o 
164.2 

355-3 
186.5 

i      1  8.2 

209.4 
40.6 
231.8 

63.5 

254-7 

85-9 

277.0 

108.1 

1865 
1866 
1867 
18685 
1869 
1870 
1871 
18725 

1873 
1874 
1875 
1876^ 
1877 
1878 
1879 
1880^6 
1881 
1882 
1883 
1884.2 
1885 
1886 
1887 
1888^ 
1889 
1890 
1891 
1892^ 

1893 
1894 
1895 
1896^ 
1897 
1898 
1899 
1900 

[9] 


TABLE   I.—  CONCLUDED. 

Aguments  of.  the  Perturbations  for  the  Different  Years. 

(Referred  to  the  Meridian  of  Wafhington.) 

Year. 

28. 

29. 

30. 

31. 

32. 

33. 

34. 

35. 

36. 

37. 

1850 

204.8 

78.8 

149.0 

1  6.2 

312.9 

353-1 

227.9 

79-5 

6-5 

47.8 

1851 

285.9 

310.9 

209.0 

338.6 

335-9 

104.5 

159.9 

341-2 

I95-9 

326.0 

18525 

7.2 

183.6 

269.2 

301.8 

o.o 

216.2 

92.8 

243-7 

26.0 

244.9 

1853 

88.3 

55-6 

329.2 

264.2 

23.0 

327.6 

24.8 

H5-4 

215.5 

163.1 

1854 

169.4 

287.7 

29.2 

226.6 

46.1 

79.0 

316.9 

47-i 

45-o 

81.3 

1855 

250.4 

159-7 

8^.2 

189.0 

69.1 

190.5 

248.9 

308.8 

234-5 

359-5 

18565 

331-7 

32-4 

H°-3 

152.2 

93-2 

302.2 

181.8 

21  1.3 

64.6 

278.4 

1857 

52.8 

264.5 

209.3 

1  14.6 

I  1  6.2 

53-6 

113.8 

II3.0 

254.1 

196.6 

1858 

133-9 

'36.5 

269.3 

77-0 

139.2 

165.0 

45-9 

H-7 

83.6 

114.7 

1859 

215.0 

8.6 

329-3 

39-4 

162.3 

276.4 

337-9 

276.5 

273.1 

32.9 

1  860  B 

296.3 

24*  -3 

29.4 

2.6 

186.3 

28.2 

270.8 

178.9 

103.2 

311.8 

1  86  1 

174 

11  3-3 

894 

325.0 

209.3 

139.6 

202.9 

80.6 

292.7 

230.0 

1862 

98.5 

345-4 

149.4 

287-4 

232.4 

251.0 

134-9 

342.4 

122.2 

148.2 

1863 

179-5 

217.4 

209.4 

249-7 

255.4 

2.4 

67.0 

244.1 

3II.8 

66.3 

18645 

260.9 

90.1 

269.5 

213.0 

279-5 

114.1 

359-8 

146.5 

I4I.8 

345-3 

1865 

34J-9 

322.2 

329-5 

175-4 

302.5 

225-5 

291.9 

48.2 

331-3 

263.5 

1866 

63.0 

194.2 

29.5 

137-8 

325.5 

337-0 

223.9 

310.0 

160.8 

iSi.6 

1867 

144.1 

66.3 

89.5 

IOO.I 

348.5 

88.4 

156.0 

211.7 

350-4 

99-8 

18685 

225.4 

299.0 

149.6 

63.4 

12.6 

200.1 

88.8 

1  14.2 

180.4 

18.7 

1869 

306.5 

171.0 

209.6 

25.8 

35-6 

3H-5 

20.9 

15.9 

9-9 

296.9 

1870 

27.7 

43-i 

269.6 

348.1 

58.6 

63.0 

312.8 

277.5 

'99-5 

215.1 

1871 

108.8 

275.1 

329.6 

310.5 

81.6 

174.4 

244.9 

179.2 

29.0 

133.3 

18725 

190.1 

147.8 

29.8 

273.7 

105.7 

286.1 

177.7 

81.7 

219.0 

52.2 

i8?3 

271.2 

19.9 

89.8 

236.1 

128.7 

37-5 

109.7 

343-4 

48.5 

330.4 

1874 

352-3 

251.9 

149.8 

198.5 

151.8 

148.9 

41.8 

245.1 

238.0 

248.6 

1875 

73-3 

124.0 

209.8 

160.9 

174.8 

260.3 

333-8 

146.9 

67.6 

1  66.8 

18765 

154.6 

356-7 

270.0 

124.1 

198.9 

12.  1 

266.7 

49-3 

257.6 

85.7 

1877 

235-7 

228.7 

33°-° 

86.5 

221.9 

'23.5 

198.8 

311.0 

87.1 

3-9 

1878 

316.8 

100.8 

30.0 

48.9 

244-9 

234-9 

130.8 

212.8 

276.6 

282.0 

1879 

37-9 

332-8 

90.0 

"-3 

267.9 

346.3 

62.8 

II4.5 

106.2 

2O0.2 

i88o5 

119.2 

205.6 

150.1 

334-5 

291.9 

98.0 

355-7 

16.9 

296.3 

II9.I 

1881 

200.3 

77.6 

210.  1 

296.9 

3  1  4-9 

209.4 

287.8 

278.6 

125.8 

37-3 

1882 

281.4 

3°9-7 

270.1 

259-3 

338.o 

320.8 

219.8 

180.4 

3I5-3 

3*5-5 

1883 

2.4 

181.7 

33°-I 

221.7 

I.O 

72.2 

151.8 

82.1 

144.9 

233-6 

18845 

83-7 

54-4 

3°-3 

185.0 

25.1 

183.9 

847 

344-5 

334-9 

152.6 

1885 

164.8 

286.5 

9°-3 

H7-3 

48.1 

295-3 

16.7 

246-3 

164.4 

70.8 

1886 

245.9 

158.5 

I50-3 

109.7 

71.1 

46.8 

308.8 

148.0 

353-9 

348.9 

1887 

327.0 

30.6 

210.3 

72.0 

94.1 

158.2 

240.8 

49-7 

183-5 

267.1 

18885 

48.3 

263.3 

270.3 

35-3 

118.2 

269.9 

173-7 

312.2 

13-5 

1  86.0 

1889 

129.4 

'35-3 

330-3 

357-7 

Hi  -3 

21.3 

105.7 

213.9 

203.0 

104.2 

1890 

210.5 

7-4 

304 

320.0 

!64-3 

132.6 

37-8 

1  15.6 

32.5 

22.4 

1891 

291.6 

239-4 

90.4 

282.4 

187-3 

244.0 

329-9 

17-3 

222.O 

300.6 

18925 

12.9 

112.  1 

150.6 

245.6 

211.4 

355-7 

262.7 

279-8 

52.1 

219.5 

'893 

94.0 

344-2 

2IO.6 

208.0 

234-4 

107.1 

194.7 

181.5 

241.6 

137-7 

1894 

175.1 

216.2 

270.6 

170.4 

257-5 

218.5 

126.8 

83.2 

7I.I 

55-9 

1895 

256.1 

88.3 

330.6 

132.8 

280.5 

329-9 

58.8 

345-o 

260.6 

334-1 

18965 

337-4 

321.0 

30.7 

96.0 

304.6 

81.7 

351-7 

247.4 

90.7 

253.0 

1897 

58.5 

193.0 

90.7 

58.4 

327.6 

J93-I 

283.7 

149.1 

280.2 

171.2 

1898 

139.6 

65.1 

150.7 

20.8 

350.6 

304-5 

215.8 

50.9 

1097 

89-3 

1899 

220.7 

297.1 

210.7 

343-2 

13.6 

55-9 

147.9 

312.6 

299.2 

7-5 

1900 

301.8 

169.2 

270.7 

305-5 

36.7 

167.4 

79-9 

214-3 

128.7 

285.7 

[10] 


TABLE   II. 

Variation  of  the  Arguments  for  the  Different  Months. 

^••••••••i 

1. 

.i^—OM^M""" 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

" 

January  .  .  . 
February.  . 
March  
April  

o.ooo 

5-991 

11402 

17.394 
23.192 

29.183 

34-98  i 
40.972 

46.963 
52.761 
58.752 
64.550 

o.ooo 

3.415 

6.500 

9.916 

13.221 

16.636 
19.941 

23-357 

26.772 

30.077 

33-493 
36.798 

o.ooo 
9.406 

17-903 
27.309 

36.412 

45.818 
54.921 

64.328 

73-734 
82.837 
92.244 
101.347 

o.ooo 

2-575 
4.902 

7-477 
9.970 

12.545 
15.038 
17.613 
20.189 
22.681 
25.257 
27.749 

o.ooo 
0.840 

J-599 
2.438 

3-251 
4.091 

4.904 

5-744 
6.584 

7-397 
8.236 

9-°49 

o.oo 
i-74 
3-3° 
5.04 
6.72 
8.46 
10.14 
11.87 
13.61 
15.29 
17.02 
18.70 

0.00 

0.90 

1.71 

2.60 

3-47 
4.36 

5-23 
6.13 

7.02 
7.89 

8.79 
9.65 

o.oo 

4.25 

8.10 

12.35 
16.47 
20.73 
24.85 

29.10 
33-35 
37-47 
4I-73 
45-85 

O.OO 

15.40 
29.31 
44.70 
59.60 

75-0° 
89.90 

105.30 
1  20.70 
135.60 
1  5  1  .00 
165.90 

o.ooo 

8.567 

16.304 
24.871 

33.161 
41.728 

50.018 

53.585 
67.151 

75-441 
84.008 

92.298 

o.oo 

20.55 

39-11 
59.66 

79-55 

JOO.IO 

119.98 

140.53 

161.08 
180.97 
201.52 
221.40 

May  

Tune  ...... 

Tuly.  .  . 

j  uv  •  •  • 
August  — 

September. 
October  .  . 
November. 
December  . 

TABLE  III. 

Variation  of  the  Arguments  for  the  Different  Days. 

•M^BMBtai^BI 

Days. 

««—  —  — 
1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

i 

0.193 

O.IIO 

0.303 

0.083 

0.02  7 

0.06 

0.03 

0.14 

0.50 

0.276 

0.66 

2 

0.387 

O.22O 

0.607 

0.166 

0.054 

O.I  I 

0.06 

0.27 

0.99 

0.552 

'•33 

3 
4 

6 

7 
8 

9 

10 

20 

0.580 

0-773 
0.966 
1.160 

1.353 
1.546 
1.740 

1-933 
3.866 

o-3  3  1 

0.441  . 
0.551 

0.66  1 

0.771 
0.882 
0.992 

I.IO2 
2.204 

0.910 
1.214 

1.517 
1.820 
2.124 
2.427 
2.731 

3-034 
6.068 

0.249 

0.332 
0.415 
0.499 
0.582 
0.665 
0.748 
0.831 
1.662 

o.o  8  1 
0.108 

0-135 
0.163 
0.190 
0.217 
0.244 
0.271 
0.542 

0.17 

0.22 
0.28 

o-34 
0-39 
0.45 
0.50 
0.56 

1.  12 

0.09 

0.12 
O.I4 
0.17 
O.2O 
0.23 
O.26 
0.29 
0.58 

0.41 
0.55 
0.69 
0.82 
0.96 

I.IO 

1.23 

1-37 
2.74 

1.49 
1.99 

2-49 
2.98 

348 
3.98 
4-47 
4-97 
9-94 

0.829 
1.105 
1.381 
1.658 
!-934 

2.2  1  I 

2.487 
2.763 
5.527 

.  *-99 
2.65 

3-3  * 
3.98 
4.64 

5-30 
5-97 
6.63 
13.26 

3° 

5-799 

3-3°6 

9.102 

2-493 

0.813 

1.68 

0.87 

4.11 

14.91 

8.290 

19.89 

TABLE   IV. 

Variation  of  the  Arguments  for  the  Different  Hours. 

Hours. 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

I 

0.008 

0.005 

0.013 

0.003 

O.OO  I 

o.oo 

o.oo 

o.oo 

O.O2 

O.OI  I 

0.03 

2 

3 
4 
5 
6 

o.oi  6 
0.024 
0.032 
0.040 
0.048 

0.009 
0.014 
0.018 
0.023 
0.028 

0.025 
0.038 
0.050 
0.063 
0.076 

0.007 

O.OIO 

0.014 

0.017 

0.021 

O.OO2 
O.O03 
O.OO5 
O.OO6 
O.OO7 

o.oo 

O.OI 
O.OI 
O.OI 
O.OI 

0.00 

o.oo 
o.oo 

O.OI 
O.OI 

O.OI 
O.02 
O.O2 
0.03 
0.04 

O.O4 
O.o6 
0.08 
O.IO 
0.12 

0.023 
0.034 
0.046 
0.058 
0.069 

0.05 
0.08 

O.I  I 

0.13- 
0.16 

7 
8 

9 
10 

0.056 
0.064 
0.072 
0.080 

0.032 
0.037 
0.041 
0.046 

0.088 

O.IOI 

0.113 
0.126 

0.024 
O.O28 
0.031 
0.035 

O.OO8 
O.OO9 
O.OIO 
0.0  1  I 

O.02 
O.O2 
O.O2 
0.02 

O.OI 
O.OI 
O.OI 
O.OI 

0.05 
O.05 
O.o6 
O.o6 

0.14 
0.17 
0.19 
0.21 

0.080 
0.092 
0.103 
0.115 

0.19 

O.22 
0.25 
0.28 

20 

o.i  60 

0.092 

0.252 

0.070 

0.023 

O.05 

0.03 

0.12 

0.42 

0.230 

0.55 

[11] 


TABLE   II.  —  CONTINUED. 

Variation  of  the  Arguments  for  the  Different  Months. 

12. 

13. 

14. 

15. 

16. 

17. 

18. 

19. 

20. 

21. 

22. 

23. 

24. 

January  .  .  . 

0.00 

0.00 

o.oo 

0.00 

0.00 

o.oo 

o.o 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

February.  . 

12.82 

7.67 

6.49 

14.56 

7-53 

1.04 

I  I.I 

5.5 

21.4 

14.0 

4.3 

23.1 

J3-7 

March  

2440 

14.60 

12.36 

27.71 

H-33 

1.97 

21.2 

10.4 

40.7 

26.7 

8.2 

44.0 

26.1 

April 

37.22 

22  27 

18.85 

4.2.27 

21.86 

3.OI 

32.3 

15.8 

62.1 

40.7 

12.  C 

67.1 

3Q.8 

May  

j  1  ' 
4-0.6  3 

""'"  i 
2Q,6Q 

2C.I  3 

T     "      / 

C6.3C 

2Q.i  <: 

j' 

4-.OI 

J    *  j 
43.1 

J. 
21.  1 

82.8 

T     "  / 

H.3 

j 
l6.7 

/  • 

89.5 

J7 

1:3.1 

June  

T7*     J 

62.4.6 

7'  7 
37.36 

j*    J 
3  1.62 

J     '  Jj 

70.01 

7'    j 
36.68 

T* 

;.O5 

T^  J 
C4.2 

26.6 

104.2 

j 

68.3 

*  / 

2I.O 

y  j 

I  12.6 

j  j 
66.8 

July.  .  . 

T 

74.87 

j  i  '  j" 

A.A..7Q 

j 
37.01 

/        7 

8c.oo 

j 
4-3.Q6 

j     j 

6.06 

J    \ 
6C.O 

31.9 

I 

124.0 

81.9 

2C.  2 

1  1C.O 

80.  i 

August  — 

/  T*      / 
87.69 

TT*/  7 

52.46 

3fy 

44.40 

j  • 
99.56 

TJ.-7 
51-49 

7.09 

J  * 

76.1 

J        7 

37-3 

T^  y 

146.3 

y 

95-9 

j  • 
29.5 

J  J 

158.1 

93-8 

September. 

100.51 

60.13 

50.90 

114.1  1 

59.02 

8.13 

87.3 

42.8 

167.7 

109.9 

33-8 

181.2 

107.5 

October.  .  . 

112.92 

67.55 

57.18 

128.20  66.31 

9-13 

98.1 

48.1 

188.4 

I23-5 

38.0 

203.6 

120.8 

November. 

12574 

75.22 

63.67 

142.76 

73.84 

10.17 

109.2 

53-6 

209.8 

137.5 

42.3 

226.7 

134-5 

December  . 

138.15 

82.65 

69.96 

156.85 

8I.I3 

11.17 

120.0 

58.8 

230.5 

151.1 

46.5 

249.1 

147.8 

TABLE   III.—  CONTINUED. 

Variation  of  the  Arguments  for  the  Different  Days. 

Days. 

12. 

13. 

14. 

15. 

16. 

M« 

18. 

19. 

20. 

21. 

22. 

23. 

24. 

I 

0.41 

0.25 

0.21 

0.47 

0.24 

0.03 

0.4 

O.2 

0.7 

0.4 

O.I 

0.7 

0.4 

2 

0.83 

0.49 

0.42 

0.94 

0.49 

0.07 

0.7 

0.4 

1-4 

0.9 

°-3 

».| 

0.9 

3 

1.24 

0.74 

0.63 

1.41 

0-73 

O.IO 

I.I 

0.5 

2.1 

i-3 

0.4 

2.2 

1-3 

4 

1.66 

0.99 

0.84 

1.88 

0.97 

0.14 

1.4 

0.7 

2.8 

1.8 

0.6 

3-° 

1.8 

5 

2.0*7 

1.24 

1.05 

2-35 

1.  21 

0.17 

1.8 

0.9 

3-5 

2.2 

0.7 

3-7 

2.2 

6 

2.48 

.  1.48 

1.25 

2.82 

1.46 

0.20 

2.2 

.1 

4-i 

2.7 

0.8 

4-4 

2.6 

7 

2.90 

»-73 

1.46 

3-29 

1.70 

0.24 

2-5 

•3 

4-8 

3-1 

I.O 

5-2 

3-1 

8 

3-3i 

1.98 

1.67 

3-76 

1.94 

O.27 

2.9 

•4 

5-5 

3-6 

i.i 

5-9 

3-5 

9 

3-73 

2.22 

1.88 

4.23 

2.19 

0.31 

3-2 

.6 

6.2 

4.0 

i-3 

6-7 

4.0 

10 

4.14 

2.47 

2.09 

4.70 

2-43 

0-34 

3.6 

.8 

6.9 

4-5 

1.4 

7-4 

4-4 

20 

8.28 

4.94 

4.18 

9.40 

4.86 

0.68 

7.2 

3-6 

13.8 

9.0 

2.8 

14.9 

8.8 

3° 

12.42 

7.41 

6.27 

14.10 

7-29 

1.02 

10.8 

5-4 

20.7 

13-5 

4.2 

22.3 

13.2 

TABLE   IV.—  CONTINUED. 

Variation  of  the  Arguments  for  the  Different  Hours. 

Hours. 

12. 

13. 

14. 

15. 

16. 

17. 

18. 

19. 

20. 

21. 

22. 

23. 

24. 

i 

0.02 

O.OI 

O.OI 

O.O2 

O.OI 

o.oo 

o.o 

o.o 

0.0 

o.o 

o.o 

o.o 

o.o 

2 

0.03 

O.O2 

0.02 

0.04 

0.02 

o.oo 

0.0 

0.0 

O.I 

0.0 

0.0 

O.I 

o.o 

3 

0.05 

0.03 

O.O3 

O.o6 

0.03 

o.oo 

o.o 

0.0 

O.I 

o.o 

o.o 

O.I 

0.0 

4 

O.O7 

0.04 

0.03 

0.08 

0.04 

o.oo 

0. 

o.o 

O.I 

0. 

0.0 

O.I 

O.I 

5 

0.08 

0.05 

0.04 

O.IO 

0.05 

O.OI 

o. 

0.0 

O.I 

o. 

o.o 

O.I 

O.I 

6 

0.10 

O.o6 

0.05 

0.12 

0.06 

O.OI 

0. 

o.o 

0.2 

o. 

o.o 

O.2 

O.I 

7 

O.I  2 

0.07 

O.o6 

0.14 

O.O7 

O.OI 

0. 

O.I 

O.2 

0. 

0.0 

0.2 

O.I 

8 

0.14 

0.08 

0.07 

o.i  6 

0.08 

O.OI 

o. 

O.I 

0.2 

o. 

o.o 

0.2 

O.I 

9 

O.I5 

0.09 

0.08 

0.18 

O.09 

O.OI 

0. 

O.I 

O.2 

o. 

0.0 

O.2 

O.I 

10 

0.17 

O.IO 

0.09 

O.2O 

O.IO  . 

O.OI 

O.2 

O.I 

0-3 

O.2 

0.0 

°-3 

O.2 

20 

o-34 

O.2I 

0.18 

°-39 

0.20 

0.02 

°-3 

O.2 

0.6 

°-3 

O.I 

0.6 

0.3  , 

[12] 


TABLE   II.—  CONCLUDED. 

Variation  of  the  Arguments  for  the  Different  Months. 

••••^••••iM* 

•••I^M 
25. 

«—«—•• 
26. 

•B«Hn« 

27. 

HiH^BHi 

28. 

m^nmxatma. 

29. 

•M«M 

30. 

»—Mi 

31. 

.«—  •- 

32. 

/™™«™c—  i 

33. 

34. 

35. 

36. 

37. 

January  .  .  . 
February.  . 
March  
April  

o.o 
26.5 
50.5 
77.0 
102.7 
129.3 
155.0 
181.5 
208.0 

233-7 
260.2 

285.9 

o.o 

16.3 
31.0 

47-3 
63.1 

79-4 
95.1 
111.4 

127.7 

H3-5 
159.8 

i75  5 

0.0 
I  6.2 

3°-9 
47.1 
62.9 
79.1 
94-8 

I  I  I.O 

127.2 
143.0 
159.2 

174.9 

o.o 
6-9 
I3-1 

20.  6 

26.7 

33-6 
40.2 
47.1 
54.0 
60.7 

67.5 

74.2 

o.o 
19.7 

37-5 
57-2 
76.3 
96.0 
115.1 
134.8 

154-5 

173.6 

193-3 
212.3 

o.o 

5-i 

9-7 
14.8 

19.7 

24.8 
29.8 

34-9 
40.0 

44-9 
50.0 

54-9 

o.o 

27.4 
52.1 

79-5 
1  06.0 

133-4 
159-9 
187.3 
214.6 

241.1 
268.5 
295.0 

o.o 

32.5 

61.9 

94-4 
125.9 
158.4 
189.9 
222.5 
255.0 
286.5 
319.0 
35°-5 

o.o 

9-5 

1  8.0 

27.5 
36.6 
46.1 

55-2 
64.7 
74.2 

83-3 
92.8 

IO2.O 

o.o 
24.8 

47-2 
72.0 
96.0 

120.8 

144.8 

169.6 

194.4 
218.4 
243.2 

267.2 

o.o 

22.2 
42.3 
64.5 

86.0 
108.3 
129.8 
152.0 
174.2 
195.8 
218.0 
239-5 

0.0 

16.1 

30.6 
46.7 
62.3 
78.4 
94.0 

I  I  O.I 

126.2 

141.8 
157-9 

173-5 

o.o 
23.6 
45.0 
68.6 
91.5 
115.1 
138.0 
161.6 
185.2 
208.1 
23,1.7 
254.6 

May     .... 

July.  ,  . 

August  .... 
September. 
October  .  . 
November. 
December  . 

— 

TABLE  III.—  CONCLUDED. 

Variation  of  the  Arguments  for  the  Different  Days. 

Days. 

25. 

26. 

27. 

28. 

29. 

30. 

31. 

32. 

33. 

34. 

35. 

36. 

37. 

i 

0.9 

0.5 

0.5 

O.2 

0.6 

O.2 

0.9 

I.O 

o-3 

0.8 

0.7 

0.5 

0.8 

2 

1.7 

j 

I.O 

I.O 

0.4 

1.3 

o-3 

1.8 

2.1 

0.6 

1.6 

1.4 

I.O 

x 

i-5 

2.6 

1.6 

1.6 

0.7 

1.9 

0.5 

2-7 

3.1 

0.9 

2-4 

2.1 

1.6 

2-3 

4 

3-4 

2.1 

2.1 

0.9 

2-5 

0.7 

3-5 

4.2 

1.2 

3-2 

2.9 

2.1 

3-° 

i 

5 

4-3 

2.6 

2.6 

I.I 

3-2 

0.8 

4-4 

5-2 

I-5 

4.0 

3-6 

2.6 

.  f. 

6 

i     -J 

5.1 

3-1 

3-1 

1-3 

3-8 

I.O 

5-3 

6.3 

x-9 

4.8 

4-3 

3-i 

4.6 

7 

6.0 

3-7 

3-7 

4-4 

1.2 

6.2 

7-3 

2.2 

5.6 

5.0 

3-6 

5-3 

61 

8 

6.8 

4-2 

4.2 

1.8 

5-i 

1.3 

7-1 

8.4 

2-5 

6-4 

5-7 

4-2 

.i 

60 

9 

7-7 

4-7 

4-7 

2.0 

5-7 

1.5 

8.0 

9.4 

2.8 

7.2 

•c6'4 

4-7 

.0 

n  A 

10 

8  "C 

5.2 

2.2 

6-3 

1.6 

8.8 

10.5 

3-1 

8.0 

7.1 

5-2 

7.0 

20 

3° 

"O 
I7.I 

25.6 

10.5 

15-7 

10.5 

'5-7 

4-4 
6.6 

12.7 
19.1 

3-3 
4-9 

17.7 
26.5 

21.0 

6.2 

9-3 

16.0 
24.0 

14-3 
21.5 

10.4 
15.6 

15.2 
22.8 

TABLE   IV.  —  CONCLUDED. 

Variation  of  the  Arguments  for  the  Different  Hours. 

Hours. 

25. 

26. 

27. 

28. 

29. 

30. 

31. 

32. 

33. 

34. 

35. 

36. 

37. 

i 

o.o 

o.o 

o.o 

o.o 

o.o 

o.o 

o.o 

0.0 

0.0 

o.o 

o.o 

o.o 

0.0 

2 

O.I 

0.0 

0.0 

o.o 

o.o 

o.o 

O.I 

O.I 

0.0 

O.I 

O.I 

0.0 

O.I 

•3 

O.I 

o. 

o. 

0.0 

O.I 

o.o 

O.I 

O.I 

0.0 

O.I 

O.I 

o. 

O.I 

j 
A. 

O.I 

o. 

o. 

o.o 

O.I 

o.o 

O.I 

0.2 

0.0 

O.I 

O.I 

0. 

O.I 

T 

c 

O.2 

o. 

0. 

o.o 

O.I 

o.o 

0.2 

O.2 

0. 

0.2 

O.I 

o. 

O.2 

J 

6 

O.2 

o. 

o. 

0.0 

O.I 

o.o 

0.2 

0.2 

0. 

0.2 

0.2 

o. 

O.2 

1 

0.2 

0. 

0. 

o.o 

0.2 

o.o 

O.2 

O.2 

o. 

O.2 

0.2 

o. 

O.2 

/ 

8 

0-3 

0.2 

0.2 

O.I 

0.2 

O.I 

0-3 

0-3 

o. 

0-3 

O.2 

O.2 

0-3 

q 

*S 

0.3 

0.2 

O.2 

O.I 

O.2 

O.I 

0-3 

0-3 

o. 

o-3 

°-3 

O.2 

o-3 

y 
IO 

J 

0.4 

0.2 

0.2 

O.I 

0.2 

O.I 

0.4 

0.4 

0. 

°-3 

o-3 

0.2 

°-3 

2O 
- 

0.8 

0.4 

0.4 

0.2 

0.5 

0.2 

0.8 

0.8 

o-3 

0.7 

0.6 

0.4 

o, 

__ucm>w> 

[13] 


TABLE  V. 

Perturbations  of  the  Mean  Anomaly. 

Argument  1. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

0° 

I 

2 

3 

227.02 
223.00 
219.08 
215.24 

4.02 

3.92 
3.84 
3-74 

45° 
46 

47 
48 

164.49 
165.96 
167.51 
169.15 

1.47 
i.55 
1.64 
1.73 

\   90° 
91 
92 
93 

255.80 
256.85 

257.81 
258.66 

i.o5 
0.96 
o.85 
0.76 

'35° 
136 

137 
'38 

200.46 
197.12 
193.72 
190.25 

3.34 
3.40 
3.47 

3.52 

4 

21  1.50 

3.65 

49 

170.88 

1.81 

94 

259.42 

o.65 

139 

186.73 

3.58 

5 

207.85 

5o 

172.69 

95 

260.07 

140 

183.15 

3.55 

1.89 

o.55 

3.63 

6 

7 
8 

204.30 
2OO.86 
197.52 

3.44 
3.34 

3.22 

5i 

52 
53 

174.58 
176.54 
178.56 

1.96 

2.02 
2.O8 

96 

97 
98 

260.62 
261.06 
261.40 

0.44 
o.34 

O  23 

141 

142 

'43 

179.52 
175.84 
172.11 

3.68 
3.73 
•3  __ 

9 

194.30 

3.12 

54 

180.64 

2.l5 

99 

261.63 

O  1  2 

144 

168.34 

*>T7 

1  Ro 

10 

I9I.I8 

55- 

182.79 

IOO 

261.75 

'45 

164.52 

V.Q3I 

3.oo 

2.20 

O.OI 

3.86 

n 

12 

13 

188.18 
185.31 
182.56 

2.87 

2.75 
2.63 

56 

57 
58 

184.99 
187.24 
189.52 

2.25 
2.28 

2.33 

IOI 
102 

I03 

261.76 

261.66 

261.45 

0.10 
0.21 
O.32 

146 

'47 
148 

160.66 

I56.774 
152.85 

3.89 
3.92 
3.g5 

»4 

1  79-93 

2.5o 

59 

191.85 

2.36 

104 

261.13 

0.43 

'49 

148.90 

3.OT 

15 

17743 

60 

194.21 

I05 

260.70 

150 

'44-93 

***T  / 

2.37 

2.39 

o.54 

4.00 

16 

«7 

18 

'9 

20 

175.06 
172.82 
170.71 
168.73 
166.89 

2.24 
2.  II 
•  1.98 
1.84 

61 
62 
63 
64 
65 

196.60 
199.01 
201.43 
203.87 
206.32 

2.41 
2.42 
2.44 
2.45 

1  06 

I07 

108 
109 

I  IO 

260.16 

259.51 

258.75 
257.89 

256.91 

o.65 
0.76 
0.86 
0.98 

'5' 
152 

'53 
'54 
'55 

'40-93 
136.92 
132.89 
128.86 
124.81 

4.01 
4-o3 
4.o3 
4.65 

1.70 

2.45 

1.09 

4-o5 

21 
22 

23 
24 

165.19 
163.62 
162.19 
160.90 

1.9] 

i.43 
1.29 
i.iS 

66 
67 
68 
69 

208.77 
211.  21 
213.64 
2l6.o6 

2.44 
2.43 
2.42 
2.41 

in 

112 

"3 

114 

255.82 
254.63 
253-33 
251.93 

1.19 
i.3o 
1.40 
i.5i 

156 

'57 
158 

'59 

120.76 
1  16.71 
1  12.66 
108.62 

4.o5 
4-o5 
4.o4 
4.o3 

25 

159-75 

70 

218.47 

"5 

250.42 

1  60 

104.59 

I.OI 

2.38 

1.62 

4.02 

26 

27 

158.74 
157.87 

0.87 

O.74 

7' 
72 

220.85 
223.19 

2.34 

2.3l 

116 
117 

248.80 
247.08 

1.72 
1.81 

161 
162 

100.57 
96.58 

3.99 

Q  -- 

28 

I57.I3 

O.l)0 

73 

225.50 

o  oft 

118 

245.27 

163 

92.61 

O-97 
1  ^/ 

29 
3° 

156.53 
156.07 

0.46 

74 
75 

227.78 
230.02 

2.  2O 
2.24 

119 

120 

243.35 
241.33 

1.92 

2.02 

164 
165 

88.67 
84-76 

J.94 
S.gl 

0.32 

2.19 

2.12 

3.88 

3» 

15575 

76 

232.21 

121 

239.21 

1  66 

80.88 

30  / 

32 

155.56 

0.  If) 

o.o5 

77 

234-34 

2.12 

1  nQ 

122 

237.00 

2.21 

2.3o 

167 

77.04 

.04 

7  Tft 

33 
34 

'55-51 

155.58 

0.07 

O.2I 

78 
79 

236.42 
238.44 

«c.OO 
2.02 

123 

I24 

234.70 

232.31 

2.39 

2/n 

168 
169 

73.26 
69.52 

-J.J& 

3.74 
1  in 

35 

1  55-79 

80 

240.41 

1-97 

125 

229.82 

•49 

170 

65.82 

*j.^\j 

o.34 

1.89 

2.58 

3.64 

36 
37 
38 

39 

40 

156.13 
156.59 

I57-I7 
157.88 
158.71 

0.46 
o.58 
0.71 
o.83 

81 

82 

83 
84 

85 

242.30 
244.12 
245.87 

247-54 

249-  '3 

1.82 
I.75 
1.67 

i.5g 

126 
I27 
128 
129 
I30 

227.24 
224.58 

221.84 
219.02 

2  1  6.  1  I 

2.66 
2.74 
2.82 
2.91 

171 
172 
'73 
'74 
'75 

62.18 
58.62 
55.12 
51.69 
48.32 

3.56 
3.5o 
3.43 
3.37 

0.94 

i.5i 

2.99 

3.28 

41 

42 

43 

159.65 
160.71 
161.86 

i.  06 
i.tS 

1  .  26 

86 

8? 
88 

250.64 
252.07 
253.40 

1.43 
1.33 

In  / 

131 
132 

'33 

213.12 
210.07 
206.94 

3.o5 
3.i3 

1  11 

176 

'77 
178 

45.04 
41.84 
38.74 

3.20 

3.io 
i  n9 

44 

45 

163.12 
164.49 

i.37 

89 
90 

254.64 
255.80 

•  24 
1.16 

'34 
'35 

203.73 

200.46 

O.  2  I 

3.27 

'79 
1  80 

35.72 
32.80 

9«m 
2.92 

[14] 


TABLE  V.  —  CONTINUED. 

Perturbations  of  the  Mean  Anomaly. 

Argument  1.  —  Concluded- 

•P^MBMM 

Arg. 

•^^••••i 
Eq. 

•MB—— 

D. 

^m^mxm^*^*— 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

t 
D. 

Arg. 

Eq.    . 

/•• 

D. 

180° 
181 
182 

183 

184 
185 

32.80 
29.98 
27.27 
24.67 
22.17 
19.79 

2.82 
2.71 
2.60 

2.5o 
2.38 

225° 
226 
227 
228 
229 
230 

50.95 
55-15 

59-5° 
63-99 
68.63 

73-41 

4.20 

4.35 
4-49 
4-64 
4-78 

/  rtO 

270° 
271 
272 

273 
274 
275 

316.90 
322.51 
328.00 
333.38 
338.63 
343-77 

5.6i 

5.49 
5.38 
5.25 
5.i4 
5.oo 

3i50 
316 

317 

318 

3»9 

320 

407.60 
405.44 
403.12 
400.66 
398.04 
395-27 

2.16 

2.32 
2.46 
2.62 

2.77 

2.92 

1  86 
187 
188 
189 
190 

17-53 
15.40 
13.40 
11.52 
9.78 

2.26 

2.l3 
2.OO 

1.88 
1.74 

231 
232 

233 
234 

235 

78-33 
83.37 
88.53 
93.82 

99-23 

4.92 

5.o4 
5.i6 
5.29 
5.4i 

R  K3 

276 
277 
278 
279 
280 

348.77 
353.63 
358.34 
362.91 

367-33 

4-86 

4-71 
4.57 
4-42 

4.26 

321 
322 
323 
324 
325 

392.35 
389-3I 
386.14 
382.84 

379-41 

3.O4 

3.17 

3.3o 
3.43 

3.55 

191 
192 
!93 
*94 
*95 

8.18 
6.72 

5-41 
4.25 

3-23 

i.  60 

1.46 
i.3i 
1.16 
i.  02 

236 

237 
238 

239 
240 

104.76 
110.38 
ii6.n 
121.93 
127.85 

J.J\j 

5.62 

5.73 
5.82 
5.92 

281 
282 
283 

284 
285 

37M9 

375-69 
379-62  , 
383-38 
386.98 

4.10  " 
3.93 
3.76 
3.6o 

3.42 

326 

327 
328 

329 
33° 

375-86 
372.21 
368.46 
364.61 
360.65 

3.65 
3.75 
3.85 
3.96 

4-o5 

196 

197 
198 

J99 

200 

2-37 
1.67 

1.  12 

0.74 
0.51 

0.86 

0.70 
o.55 
o.38 

0.23 

241 
242 
243 
244 
245 

133-86 

139-94 
146.09 
152.32 
158.61 

O.OI 

6.08 

6.i5 
6.23 
6.29 

A  TK 

286 

287 
288 
289 
290 

390.40 

393.64 
396.71 

399-59 
402.29 

3.24 
3.07 
2.88 
2.70 

2.5l 

33i 
332 
333 
334 
335 

356.60 

352.48 
348.28 
344.01 
339-66 

4.12 
4.20 
4.27 
4.35 

4.4i 

201 
2O2 
203 
204 
205 

0.46 
0.57 
0.85 
I.3I 

i-93 

o.o5 

O.I  I 

0.28 
0.46 
0.62 

_  Q.-. 

246 
247 
248 

249 

250 

164.96 

i7i-35 
177.79 
184.26 
190.77 

U.O  J 

6.39 
6.44 
6.47 
6.5i 

6.53 

291 
292 
293 
294 
295 

404.80 
407.12 
409.25 
411.18 

412.93 

2.32 
2.13 
1.93 
1.75 

i.55 

336 

337 
338 
339 
340 

335-25 
330.80 
326.30 
321.76 
W-17 

4-45 
4.5o 
4.54 
4.59 

4.62 

2O6 
2Oy 
208 
209 
2IO 

2-73 

3-7° 
4.85 

6.17 
7.67 

O.oO 

0.97 

i.i5 

1.32 

I.  JO 

251 

252 

253 
254 

255 

197.30 
203.85 
210.40 
216.95 
223.51 

6.55 
6.55 
6.55 
6.56 

296 

297 
298 

299 

300 

414.48 

4»5.83 
416.99 
417.96 

4!8-73 

i.35 
1.16 
0.97 
0.77 

r\  *\i 

341 
342 
343 
344 
345 

312.55 
307.92 

303.27 
298.61 

293.93 

4.63 
4.65 
4.66 
4-68 

4.67 

211 

212 

2I3 
214 
215 

9-35 

II.  21 

I3-24 
15-44 
17.82 

1.68 
1.86 

2.03 
2.20 
2.38 

256 

257 
258 

259 
260 

230.06 
236.58 
243.08 
249-55 
255-99 

6.55 

6.52 
6.5o 
6.47 
6.44 

A  /« 

301 
302 
3°3 
3°4 
3°5 

419.30 
419.68 
419.87 
419.87 
419.67 

0.37 

o.38 
0.19 

O.OO 
0.20 

o.3o 

346 

347 
348 
349 
35° 

289.26 
284.60 
279.95 

275-32 
270.70 

4.66 
4.65 
4.63 
4.62 

4.59 

216 

217 
218 
219 

22O 

20.38 
23.11 
26.OI 
29.07 
32.31 

2.56 

2.73 

2.90 

3.06 

3.24 

261 
262 
263 
264 
265 

262.39 

268.73 
275.01 
281.23 

287.39 

6.40 

6.34 
6.28 

6.22 
6.l6 
A  r.Q 

306 

3°7 
308 

3°9 
310 

419.28 

418.70 

4x7-94 
417.00 

|i5.87 

o.58 
0.76 
0.94 
I.i3 

i.3i 

351 
352 

353 
354 

355 

266.11 
261.56 
257.06 
252.60 
248.18 

4.55 
4-5o 
4.46 
4-42 

4.37 

221 

222 
223 
224 
225 

35-72 

39-29 
43.02 
46.90 

5°-95 

3.4i 
3.57 
3.73 
3.88 
4-o5 

266 
267 
268 
269 

270 

293-47 
299.47 

3°5-37 
311.18 
316.90 

O.OO 

6.00 
5.90 

5.8i 
5.72 

311 
312 

3'3 

3H 
3^5 

414.56 

4I3-°7 
411.42 
409.60 
407.60 

1.49 
i.65 
1.82 

2.OO 

356 
357 
358 

359 
360 

243.81 

239-5  1 
235.28 
231.12 
227.02 

4.3o 
4.23  ' 
4.16 
4.10 

[15] 


TABLE  V.  —  CONTINUED. 

Perturbations  of  the  Mean  Anomaly. 

Argument  2. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

0° 

I 

2 

161.27 

155.50 
149.81 

5.77 
5.69 

5.63 

45° 
46 

47 

1.23 

0.72 
o-37 

o.5i 
o.35 

o,  in 

90° 

91 
92 

122.  II 

127.37 
132.69 

5.26 

5.32 
5.36 

135° 
136 

137 

358.80 
362.96 
367.04 

4.16 
4.08 
4.00 

3 
4 
5 

1  44.  1  8 
138.62 

I33'i3 

5.56 
5.49 

48 
49 
5° 

0.18 
0.15 

0.27 

o.o3 

0.12 

93 
94 
95 

138.05 
1  43-46 

H8.93 

5.4i 
5.47 

138 

'39 
140 

37I-04 
374.96 
378.81 

3.92 

3.85 

5.4i 

0.28 

5.5i 

3.76 

6 

127.72 

5.33 

51 

0.55 

0.45 

96 

154.44 

5.53 

141 

382.57 

3.68 

7 

122.39 

5.25 

52 

1.  00 

O.6o 

97 

159-97 

5.56 

142 

386.25 

3.6o 

8 

117.14 

5.17 

53 

1.  60 

O.75 

98 

165-53 

5.6o 

H3 

389.85 

3.53 

9 

10 

111.97 

106.88 

/ 
5.09 

54 
55 

2-35 

3-27 

0.92 

99 

100 

171.13 

176.75 

5.62 

144 

H5 

393.38 
396.83 

3.45 

4.99 

1.07 

5.64 

3.37 

ii 

12 

101.89 
96.98 

4.91 
4.82 

56 

57 

4-34 

5-57 

1.23 

i.38 

101 

102 

182.39 
188.04 

5.65 
5.66 

146 
147 

400.20 
403.49 

3.29 
3.23 

13 

92.16 

4.72 

58, 

6.95 

i.54 

I03 

193.70 

5.67 

148 

406.72 

3.i5 

14 

15 

87.44 
82.82 

***  /  • 
4.62 

59 
60 

8-49 
10.18 

1.69 

IO4 
105 

199-37 

205.04 

5.67 

149 
150 

409.87 
412.94 

3.07 

4.52 

i.85 

5.67 

3.oo 

16 
17 

78.30 
73.88 

4.42 
/  "<<•> 

61 

62 

12.03 
14.03 

2.0O 
2  1  5 

I  06 

107 

210.71 
216.36 

5.65 
5.65 

151 
152 

415.94 

418.87 

2.93 
2.86 

18 

69.58 

4"3(J 

63 

16.18 

108 

222.OI 

5.63 

*53 

42L73 

2  IO 

19 
20 

65.37 
61.28 

4-21 
4.09 

64 

65 

18.47 
20.92 

2.29 
2.45 

109 

I  IO 

227.64 
233.26 

5.62 

'54 
155 

424.52 

427.25 

*•  /y 
2.73 

3.98 

,2.5g 

5.6o 

2.66 

21 

57-3° 

3.86 

66 

23-51 

2.74 

in 

238.86 

5.56 

156 

429.91 

2.60 

22 
23 

53-44 
49.69 

3.75 
3.62 

67 
68 

26.25 
29.12 

••  /H- 

2.87 

3.oi 

112 

IJ3 

244.42 
249.96 

5.54 
5.5i 

'57 
158 

432-51 
435-05 

2.54 
2.47 

24 
25 

46.07 
42.56 

3.5i 

69 

70 

32-13 

35-28 

3.i5 

114 
H5 

25547 
260.95 

5.48 

159 

1  60 

437.52 
439-94 

2.42 

3.38 

3.29 

5.44 

2.36 

26 
27 
28 

39.18 

35-93 
32.81 

3.25 

3.12 

3.oo 

7i 
72 
73 

38.57 
41.98 

45.52 

3.4i 
3.54 
3.66 

116 
117 

118 

266.39 
271.78 

277.12 

5.39 
5.34 
5.3o 

161 
162 
163 

442.30 
444.60 
446.86 

2.3o 
2.26 

2.21 

29 

29.81 

2.86 

74 

49.18 

1  in 

119 

282.42 

5.25 

164 

449.07 

2.l5 

30 

26.95 

75 

52.97 

0.79 

1  20 

287.67 

*5 

45  1.22 

2.73 

3.91 

5.20 

2.  II 

31 

32 

24.22 
21.64 

2.58 
2.45 

76 

77 

56.88 
60.90 

4.02 

4.  1  3 

121 
122 

292.87 
298.01 

5.i4 
5.o8 

1  66 
167 

453.33 
455.40 

2.07 
2.03 

33 

19.19 

9  7n 

78 

65.03 

4nf{ 

I23 

303.09 

5  02 

168 

457-43 

2.0O 

34 
35 

16.89 
14.72 

i.ou 
2.17 

79 
80 

69.28 
73.63 

.  JL  J 

4.35 

I24 
125 

3O8.I  I 

3  !  3-°7 

4.96 

169 

170 

459-43 
461.38 

J.95 

2.02 

4-46 

4.89 

1.92 

36 
37 
38 

12.70 
10.83 
9.10 

1.87 

i.73 
i.58 

81 
82 

83 

78.09 
82.64 
87.28 

4.55 
4.64 

4.73 

126 

127 
128 

317.96 
322.79 

327-55 

4.83 

4.76 
4.68 

171 

172 

173 

463-30 
465.18 
467.04 

£io  o  o 

1.88 
1.86 
1.84 

39 

4° 

7.52 
6.09 

1.43 

84 
85 

92.01 
96.84 

4.83 

I29 

I30 

332.23 
336.85 

4.62 

»74 

'75 

408.08 

470.69 

1.81 

1.28 

4.91 

4-54 

1.78 

4i 

42 

43 
44 
45 

4.81 
3-69 
2-73 
1.90 
1.23 

1.  12 
0.96 

o.83 
0.67 

86 

87 
88 

89 
90 

101.75 
106.73 
111.79 
1  16.91 

122.  II 

4.98 
5.o6 

5.12 

5.  20 

131 

132 

133 
134 

'35 

34M9 
345-85 
350-24 
354-56 
358.80 

4-46 
4.39 
4-32 
4-24 

176 

177 
178 
179 
1  80 

472.47 
474-24 
475.99 

477-73 
479-45 

i-77 
i.75 

1-74 
1.72 

[16] 


• 
^ 


/ 

TABLE  V.—  CONTINUED. 

Perturbations  of  the  Mean  Anomaly. 

Argument  2.  —  Concluded. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

1  80° 
181 
182 
183 

479-45 
481.16 

482.86 
484.55 

1.71 
1.70 
1.69 
i.  60 

225° 
226 
227 
228 

564.59 
566.70 
568.81 
570.90 

2.  II 
2.  II 
2.09 
2.O7 

270° 
271 
272 
273 

611.05 
6lO.OO 
608.83 
607.54 

i.o5 
1.17 
1.29 
1.42 

3!! 
$1? 

445.50 
439.58 
433.60 

427.56 

5.92 
5.98 
6.04 
6.09 

184 

486.24 

V 

1.  60 

229 

572.97 

/ 
2.06 

274 

6o6.I2 

i.55 

319 

421.47 

6.14 

185 

487.93 

i  .^V 

230 

575-03 

275 

604.57 

320 

4I5-33 

1.68 

2.O4 

1.68 

6.  20 

1  86 

489.61 

1.69 

231 

577.07 

2.02 

276 

602.89 

i.  80 

321 

409.13 

6.23 

187 

491.30 

i  .60 

232 

579.09 

2.00 

?77 

601.09 

1.94 

322 

402.90 

6.28 

188 

492.99 

i  .60 

233 

581.09 

I  O7 

278 

599^5 

2.o5 

323 

396.62 

6.3i 

189 

494.68 

i  .70 

234 

583.06 

1  *V  / 

I  C\fi 

279 

597.10 

2  .  1  0 

324 

390-31 

6.36 

190 

496.38 

235 

585.00 

i  •  iy  i 

280 

594.91 

325 

383-95 

1.70 

I.gl 

2.32 

6.39 

191 

498.08 

I  T2 

236 

586.91 

1.87 

281 

592.59 

2-44 

326 

377.56 

6.41 

192 

499.80 

••T* 

I  19 

237 

588.78 

1.84  * 

282 

590.15 

327 

37LI5 

A  /./. 

501.52 

'•7a 

238 

590.62 

1  .79 

283 

587.58 

2.  7O 

328 

364-71 

U.44 
6.46 

194 
»95 

503.26 
505.00 

1-74 

239 
240 

592.41 
594.16 

I.75 

284 
285 

584.88 
582.08 

•  / 
2.82 

329 

330 

358.25 
35L76 

6.49 

1.76 

1.70 

2.95 

6.5i 

196 

506.76 

t  TT 

241 

595.86 

1.66 

286 

579.11 

3.O7 

33i 

345.25 

652 

197 

5o8.53 

*•  /  / 
1-79 

242 

597.52 

1.59 

287 

576.04 

3.20 

332 

348.73 

6.53 

198 

510.32 

1.  8O 

243 

599.11 

i.53 

288 

572.84 

3.32 

333 

332.20 

6.54 

199 

512.12 

1.82 

244 

600.64 

1.48 

289 

569-52 

3.44 

334 

325.66 

6.55 

200 

5  i  3-94 

245 

602.12 

290 

566.08 

335 

3-19.11 

1.84 

1.42 

3.57 

6.56 

2OI 

515.78 

1.86 

246 

603.54 

i.34 

291 

562.51 

3.69 

336 

312.55 

6.55 

2O2 

517.64 

1.87 

247 

604.88 

1.28 

292 

558.82 

3.8i 

337 

306.00 

6.55 

203 

519.51 

1.90 

248 

606.16 

1.  21 

293 

555-01 

3.92 

338 

299.45 

6.54 

204 

521.41 

I  OI 

249 

607.37 

I  il 

294 

551.09 

4.04 

339 

292.91 

205 

523-32 

i  .y  i 

250 

608.50 

1  .  1  vj 

295 

547.05 

34° 

286.36 

' 

1.93 

i.o5 

4.i5 

6.53 

206 

525.25 

1.  06 

251 

609.55 

296 

542.9° 

4.26 

341 

279.83 

6.52 

207 

527.21 

V 

1.97 

252 

610.52 

0.97 
0.88 

297 

538.64 

4.37 

342 

273-31 

6.5o 

208 

529.18 

I  .90 

253 

6  1  1  .40 

298 

534-27 

A  48 

343 

266.81 

6.48 

209 

53I-I7 

2.0O 

254 

612.19 

0.79 
0.71 

299 

529.79 

/l.£lL> 

4.58 

344 

260.33 

6.47 

2IO 

533-J7 

255 

612.90 

3°° 

525.21 

345 

253.86 

2.02 

0.61 

4.69 

6.44 

21  I 

535-J9 

2.04 

256 

613.51 

O.52 

301 

520.52 

4-79 

346 

247.42 

6.41 

212   537.23 

2.o6 

257 

614.03 

3°2 

515.73 

4.88 

347 

241.01 

6.38 

213 

539-29 

2.o6 

258 

614.45 

0.42 

3°3 

510.85 

4.98 

348 

234-63 

6.35 

2I4 

541-35 

2.08 

259 

614.77 

O.32 

3°4 

505-87 

5.OT 

349 

228.28 

6.32 

215 

543-43 

260 

614.99 

0.  22 

305 

500.80 

*j.u  i 

350 

221.96 

2.10 

O.I  I 

5.i7 

6.28 

216 

545-53 

2  IO 

261 

615.10 

3°6 

495.63 

5.25 

351 

215.68 

6.24 

217 

547.63 

262 

615.10 

o.oo 

3°7 

490.38 

5.33 

352 

209.44 

6  10 

218 

549-73 

212 

263 

614.98 

O.  I  2 

308 

485.05 

5.42 

353 

203.25 

6.  1  5 

219 

551.85 

2  12 

264 

614.77 

O.2I 

C\  ^I 

309 

479.63 

5.5o 

354 

197.10 

22O 

553-97 

265 

614.46 

U.O  I 

310 

474'1  3 

355 

190.99 

2.13 

0.44 

5.59 

6.06 

221 

222 
223 

556.10 
558.22 
560.35 

2.12 
2.13 

266 
267 
268 

614.02 

613-45 
612.77 

0.57 
0.68 

e\  Qn 

312 

468.54 
462.87 
457.15 

5.67 
5.72 

t.  -Q 

356 
357 
358 

184.93 

178.93 
172.99 

6.00  • 
5.94 

^  Q/-. 

f                 S.  .  \  Z. 

224    562.47 
*t   T/    2.12 
225  i  564.59 

269 
270 

611.97 
611.05 

O.OO 

0.92 

3H* 
315 

451-37 
445-5° 

3.70 
6.87 

359 
360 

167.10 
161.27 

3.09 

5.83 

[17] 


TABLE  V.—  CONTINUED. 

Perturbations  of  the  Mean  Anomaly. 

Argument  3. 

Arg.   Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

o°   42.77 

2.66 

45° 

219.67 

x  8x 

9°°  433-37 

X  IX 

135° 

557-07 

1  .01 

i   45-43 
2   48.16 

3   50-96 

2.73 

2.80 

2  8l 

46 

47 
-48 

224.51 
229.36 
234-23 

4.04 
4.85 
4.87 

/  8r> 

91 

92 
93 

437-5  i 
441.61 

445.65 

**•  *^i 

4.10 
4.04 

136 

J37 
138 

558.08 
559.01 

559-85 

0.93 

0.84 

o  76 

4   53-83 

^.o  / 

0  f)/t 

49 

239.12 

4.09 

94 

449.64 

0.99 

3  nX 

J39 

560.61 

0.68 

5   56.77 

4.y4 

5° 

244.02 

4-9O 

?5 

453.58 

0.94 

140 

561.29 

3.01 

4.92 

3.89 

o.58 

6   59.78 
7   62.86 
8  |  66.00 
9   69.21 

10   72.49 

3.o8 
3.i4 

3.21 

3.28 

5i 

52 
*   53 
54 
55 

248.94 
253.86 

258.79 
263.73 

268.68 

4.92 
4.93 
4-94 
4.95 

96 

97 
98 

99 

IOO 

457-47 
461.31 

465-09 
468.81 
472.48 

3.84 
3.78 
3.72 
3.67 

141 
142 

H3 
144 

H5 

561.87 
562.37 
562.78 
563.11 
563-36 

o.5o 
0.41 
o.33 

0.25 

3.35 

4.95 

3.6i 

0.16 

1  1 

12 

75.84 
79.25 

3.4i 

3  Al 

56 

57 

273.63 
278.58 

4.95 
4.95 

101 
*  102 

476.09 
479-63 

3.54 
3.48 

146 

H7 

563.52 
563.60 

0.08 
o.oo 

'3 

82.72 

J.4  / 

3.53 

58 

283.53 

4.95 

103 

483.11 

3.42 

148  563.60 

O.  IO 

1.4 

86.25 

3.5g 

59 

288.48 

4.o5 

104 

486.53 

3.36 

149  563.50 

0.18 

15  ;  89.84 

60 

*293-43 

**•  y-' 

I05 

489.89 

150  563.32 

„ 

3.65 

4.95 

3.3o 

0.27 

16 

i? 

18 

9349 
97.20 
100.96 

3.7i 
3.76 
3.82 

61 
62 
63 

298.38 

303-31 
308.24 

4.93 
4-93 
4.o3 

1  06 
107 

108 

493-^9 

496.42 

499-58 

3.23 
3.i6 
3.  10 

X5' 
152 

!53 

563.05 
562.70 
562.26 

o.35 
0.44 

O.52 

'9 

104.78 

1  R8 

64 

3I3-I7 

t+.yv 
X..QI 

109 

502.68 

3.o3 

154  561.74 

'0.61 

20    108.66 

o.oo 

65 

318.08 

i*.y  i 

no 

505.71 

!55 

561.13 

3.93 

4.90 

2.96 

0.69 

21 

112.59 

66 

322.98 

X  go 

III 

508.67 

2.89 

156 

560.44 

22 

116.58 

3.99 

/  n/ 

67 

327.87 

£|.l>y 

4.88 

112 

511.56 

2.82 

J57 

559-67 

0.77 
0.86 

23 

120.62 

4.O4 
4.08 

68 

332.75 

4.86 

H3 

5H-38 

2.74 

158 

558.81 

0.94 

24 

124.70 

4tX 

69 

337.6i 

4.84 

114 

517.12 

2.68 

'59 

557.87 

i.o3 

25 

128.84 

.14 

70 

342.45 

"5 

519.80 

1  60 

556.84 

4.18 

4.82 

2.60 

i.  ii 

26 

133.02 

4.23 

7i 

347-27 

4.80 

116 

522.40 

2.53 

161 

555-73 

1.20 

27 

137.25 

4  Of 

72 

352.07 

4.78 

117 

524-93 

2.46 

.  162  554.53 

1.27 

28 

141.52 

.27 

X  "*-> 

73 

356.85 

4.76 

118 

527-39 

2.38 

163  553.26 

i.36 

29 

145.84 

4>Oz 
X  ^A 

74 

361.61 

4.  f\j 
4.73 

119 

529.77 

2.3o 

164  551.90 

1.44 

30 

150.20 

4*"U 

75 

366.34 

1  20 

532.07 

165  |  550.46 

4.40 

4.71 

2.22 

1.52 

31 

154.60 

4.44 

76 

37i-o5 

4.67 

121 

534-29 

2.l5 

1  66 

548.94 

i.  60 

32 

159.04 

4.48 

77 

375-72 

4.65 

122 

536.44 

2  O1 

167 

547-34 

1.67 

33 

163.52 

4.5i 

78 

380.37 

4.62 

123 

538.51 

£.\J  I 

168 

545-67 

1.77 

34 

168.03 

4.55 

79 

384-99 

4.5o 

124 

540.50 

'•99 

I  OI 

169 

543-9° 

i.83 

35 

172.58 

80 

389-58 

*»"-'y 

125 

542.41 

1  •  V* 

170' 

542.07 

4.58 

4.55 

1.84 

1.92 

36 

37 

177.16 
181.78 

4.62 

X  6/5 

81 
82 

394-13 
398.65 

4-52 
f.  /.R 

126 

127 

544.25 
546.00 

i.75 

T  f  iS 

171 

172 

540.15 
538.15 

2.00 
2.O7 

38 

186.42 

4.U4 
4.67 

83 

403.13 

4.40 
4.44 

128 

547.68 

1  .UO 

i.5g 

173 

536.08 

2.13 

39 

191.09 

4.70 

84 

407.57 

4.40 

129 

549-27 

V 

i.5i 

174 

533-93 

2.23 

40 

'95-79 

t+.  |V 

85 

411.97 

I30 

550.78 

175 

53^70 

4.73 

4.37 

1.42 

2.3o 

4' 

42 

200.52 
205.27 

4.75 

4.18 

86 
87 

416.34 
420.66 

4.32 
4.28 

!3' 

I32 

552.20 
553-54 

i.34 
1.26 

176 

177 

529.40 

527.03 

2.37 

2.44 

43 

210.05 

**•  /  V 

4.80 

88 

424.94 

'  /  n  / 

133 

554.80 

i  iS 

178  ;  524.59 

2.53 

44 
45 

214.85 
219.67 

4.82 

89 
90 

429.18 
433-37 

4-24 
4.19 

«34 

'35 

555-98 
557-07 

I  .  I  o 
I.Og 

179   522.06 
1  80   519.47 

2.59 

[18] 


TABLE  V.  —  CONTINUED. 

Perturbations  of  the  Mean  Anomaly. 

Argument  3.  —  Concluded. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

180° 
1  8l 

51947 
516.80 

2.67 

225° 
226 

344.18 
339-41 

4.77 
4.78 

270° 
271 

132.79 
128.66 

4.i3 
4.09 

315° 
316 

7-47 
6-39 

i.  08 

I.OO 

182 

514.07 

2.  8  1 

227 

334-63 

*#••  (** 

4.80 

272 

124.57 

4.o3 

317 

5-39 

0.91 

183 

511.26 

2.88 

228 

329-83 

4.82 

273 

120.54 

3.OQ 

3J8 

4.48 

o.83 

184 

508.38 

2.94 

229 

325.01 

4.83 

274 

116.55 

vs.yy 
3.94 

319 

3-65 

0.74 

185 

505-44 

230 

320.18 

275 

112.  6l 

320 

2.91 

3.oi 

4.85 

3.89 

0.66 

186 

502.43 

231 

315-33 

4.85 

276 

108.72 

3.84 

321 

2.25 

o.5i 

187 

499-36 

31  / 

232 

310.48 

4  87 

277 

104.88 

^  in 

322 

1.68 

v.*y  l 

0.4.3 

188 

496.22 

•  14 

3.  20 

233 

305.61 

4.87 

278 

101.09 

j.  /y 
3.73 

323 

1.20 

0.41 

189 

493.02 

234 

300.74 

t*1-'  / 
4,88 

279 

97-36 

3.68 

324 

°-79 

o.3i 

190 

489-75 

0.2*7 

235 

295.86 

280 

93.68 

325 

0.48 

3.33 

4.88 

3.62 

0.23 

191 

486.42 

i  in 

236 

290.98 

4.88 

281 

90.06 

3.56 

326 

0.25 

o.  14 

192 

483.03 

0.09 

3  /A 

237 

286.10 

282 

86.50 

3.5o 

327 

O.I  I 

o  06 

193 

479-57 

.40 

281.22 

x  88 

283 

83.00 

3.45 

328 

0.05 

o.o3 

194 

476.06 

3.57 

239 

276.34 

4*00 
4.89 

284 

79-55 

3.38 

329 

0.08 

O.I  2 

195 

472.49 

240 

271.45 

285 

76.17 

33° 

O.2O 

3.63 

4.88 

3.32 

O.2O 

196 

468.86 

3f 

241 

266.57 

/  QQ 

286 

72.85 

331 

0.40 

o.3o 

197 

465.19 

.67 

3_  , 

242 

261.69 

4.OO 

287 

69.59 

o.  2o 
Q  In 

332 

0.70 

o.38 

198 
199 

461.45 
457-66 

•74 
3.79 
3.84 

243 
244 

256.83 
251.96 

4.87 

4.85 

288 
289 

66.40 
63.27 

vj.  i  (y 

3.i3 
3.o6 

333 
334 

1.  08 

o.45 
o.55 

200 

453-82 

245 

247.11 

290 

60.21 

335 

2.08 

,-,    \ 

3.90 

4-84 

2.99 

o.63 

201 

449.92 

3.94 

246 

242  27 

4.83 

291 

57-22 

2.93 

336 

2.71 

0.71 

202 

445.98 

247 

237.44 

x  8t 

292 

54.29 

2.86 

337 

342 

0.80 

203 
204 
2O5 

441.98 
437-93 
433-84 

4>oo 
4-o5 
4.09 

248 

249 
250 

232.63 
227.82 
223.03 

l\,O  i 

4-8l 
4-79 

293 
294 
295 

5«43 

48.65 

45-93 

2.78 
2.72 

338 
339 
34° 

4.22 
5.II 
6.08 

0.89 
0.97 

4.14 

4-77 

2.65 

i.  06 

206 

429.70 

X  18 

251 

218.26 

4.75 

296 

43.28 

2.58 

341 

7.H 

1.  14 

207 

425.52 

252 

213.51 

**•  /^ 
/  "in 

297 

40.70 

342 

8.28 

1.23 

208 

421.30 

253 

208.79 

4-72 

298 

38.20 

2*  DO 

343 

9.51 

209 

417-03 

4.^7 
4.3  1 

254 

204.08 

4.71 
4.60 

299 

35-77 

2.36 

344 

10.82 

1.40 

2IO 

412.72 

255 

*99-39 

*+«"^ 

300 

33-41 

345 

12.22 

4.35 

4.67 

2.28 

1.47 

211 

408.37 

4.3g 

256 

194.72 

4.63 

301 

J«««3 

2.  2O 

346 

13.69 

1.56 

212 
213 
214 
2I5 

403.98 
399-56 

395-n 
390.62 

4.42 
4.45 
4.49 

257 
258 

259 
260 

190.09 
185.48 
180.89 

176.34 

4.61 
4.59 
4.55 

302 
303 
304 
305 

28.93 
26.80 

24-75 
22.78 

2.13 
2.05 

1.97 

347 
348 
349 
35° 

15.25 
16.89 

18.61 

20.41 

1.64 
1.72 
1.  80 

4.52 

4.52 

20.88 

1.90 

1.89 

216 

217 

218 

219 

22O 

386.10 
38L55 
376.97 
372.37 
367-73 

4.55 
4.58 
4.60 
4.64 

261 
262 
263 
264 
265 

171.82 

167.34 
162.89 

158.48 
154.10 

4-48 
4-45 
4-41 
4.38 

306 

3°7 
308 

3°9 
310 

19.07 

17-33 
15.68 
14.10 

1.81 
1-74 
i.65 
1.58 

351 

352 
353 

354 
355 

22.30 
24.26 
26.31 
28.43 
30.63 

1.96 
2.o5 

2.12 
2.20 

4.66 

4.34 

i-49 

2.28 

221 
222 

363.07 
358.38 

4.69 

266   H9.76 

267  !  145.46 

4.3o 

311 
312 

12.  6l 
11.20 

1.41 

356 
357 

32.91 
35.26 

2.35 

0   /I 

223 

353-67 

268  '  141.19 

4.27 

9.87 

1  .33 

358 

37.69 

2.40 

224 

348-9t  i* 

269  136.97 

4-22 
4.l8 

3H 

8.63 

1.24 
1.16 

359 

40.19 

2.5o 
2.58 

225 

344.18  ; 

270  132.79 

3i5 

7-47 

360  !  42.77 

[19] 


TABLE  V.  —  CONTINUED. 

Perturbations  of  the  Mean  Anomaly. 

Argument  4. 

Arg. 

Eq. 

D. 

Arg 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

o 

71.69 

0.  1  2 

45C 

28.87 

i.3o 

90 

0.65 

0.  22 

135° 

20.1  8 

0.18 

i 

7*-57 

0.18 

4'6 

27.57 

1.29 

91 

0.87 

0.24 

136 

20.36 

o.i  5 

2 

3 

71-39 
71.17 

0.22 
0.26 

47 
48 

26.28 
25.01 

1.27 

1.25 

92 
93 

I.I  I 

1.38 

0.27 

o.3o 

137 
138 

20.51 
20.63 

O.I  2 

0.09 

4 

70.91 

0.32 

49 

23.76 

1.24 

94 

1.68 

o.33 

139 

20.72 

0.06 

5 

70.59 

5° 

22.52 

95 

2.OI 

140 

20.78 

O.37 

1.  21 

o.35 

o.o3 

6 

70.22 

O.4l 

51 

21.31 

I.I9 

96 

2.36 

o.38 

141 

20.8  I 

o.oo 

7 

69.81 

O.46 

52 

20.12 

1.16 

97 

2.74 

0.40 

142 

20.8  I 

o.o3 

8 

69.35 

o.5i 

53 

18.96 

1.14 

98 

3-H 

0.42 

H3 

20.78 

o.o5 

9 

68.84 

o.56 

54 

17.82 

1.  1  1 

99 

3-56 

144 

20.73 

0.09 

10 

68.28 

55 

16.71 

IOO 

4.00 

' 

H5 

20.64 

0.61 

i.  08 

0.46 

0.12 

n 

67.67 

0.66 

56 

15.63 

1.  06 

101 

4-46 

0.48 

146 

20.52 

0.14 

12 

67.01 

0.70 

57 

H-57 

1.02 

IO2 

4-94 

o.5o 

H7 

20.38 

0.18 

13 

»4 
15 

66.31 

65.57 
64.78 

0.74 
0.79 

58 

59 
60 

'3-55 
12.56 
1  1.  60 

0.99 
0.96 

103 
104 
I05 

5-44 
5.96 

6-47 

0.52 

o.5i 

148 
149 
150 

20.20 

20.00 

19.78 

O.2O 
0.22 

o.83 

0.92 

0.53 

O.25 

16 

18 
»9 

20 

63.08 
62.17 
61.22 
60.24 

0.87 
0.91 
o.g5 
0.98 

61 
62 
63 
64 
65 

10.68 

9-79 
8.94 

8.12 

7-34 

0.89 

o.85 
0.82 
0.78 

106 
107 
108 
109 
no 

7.00 

7.54 
8.09 
8.64 
9.20 

o.54 
o.55 
o.55 
o.56 

'51 
152 

«54 

'9-53 
19.25 
18.95 
18.62 
18.27 

0.28 

o.3o 
o.33 
o.35 

i.  02 

0.74 

o.55 

o.36 

21 

22 
23 
24 
25 

59-22 

58.16 

57.08 

55-96 
54.82 

1.  06 
i.  08 

1.  12 

1.14 

66 
67 
68 
69 

70 

6.60 
5.90 

5-23 
4.61 
4.02 

0.70 
0.67 
0.62 
o.Sg 

in 

I  12 

115 

9-75 
10.31 

10.88 
11.44 
11.99 

o.56 
0.57 
o.56 
o.55 

156 
158 
1  60 

17.91 
17.52 
17.11 
16.68 
16.22 

o.3g 
0.41 
o.43 
0.46 

1.17 

o.54 

o.55 

0.47 

26 

53.65 

1.20 

71 

348 

o.5o 

116 

12.54 

o.55 

161 

X* 

'5-75 

0.48 

27 
28 
29 
30 

52.45 
51.24. 

50.00 

48.74 

1.  21 

1.24 

1.26 

72 
73 
74 
75 

2.98 
2.51 
2.09 
1.71 

0.47 
0.42 
o.38 

117 
118 
119 
1  20 

13.09 
13.62 
14.14 
14.66 

o.53 

0.52 
0.52 

IO2 

163 
164 
165 

15.27 
14.78 
14.28 
13.76 

0.49 
o.5o 

0.52 

1.28 

o.34 

o.5o 

o.53 

31 
32 

33 

34 

47.46 

46.16 
44.86 
43-54 

i.3o 
i.3o 

1.32 
1.32 

76 
77 
78 
79 

1.07 
0.80 
0.58 

o.3o 
0.27 

0.22 

0.18 

121 

122 
I23 
124 

15.16 

15.65 

1  6.  1  2 

.  16.57 

0.49 
0.47 
o.45 
0.44 

1  66 
167 
168 
169 

I3-Z3 
12.70 
12.17 
11.63 

o.53 
o.53 
o.54 
o.55 

35 

42.22 

80 

0.40 

I25 

17.01 

170 

1  1.  08 

i.34 

0.14 

0.42 

o.55 

36 

37 
38 

40.88 

39-55 
38.21 

1.33 
i.34 
i.35 

81 

82 
83 

0.26 
o/i  6 

O.IO 

O.IO 

0.06 
o.o3 

126 

I27 
128 

17.43 
17.83 

18.21 

0.40 
o.38 
o.36 

171 
172 

9-99 
9-45 

o.54 
o.54 
o.54 

39 

36.86 

84 

0.07 

129 

18.57 

o  33 

'74 

8.91 

o.53 

40 

35-52 

1.34 

85 

0.08 

O.O  I 

130 

18.90 

175 

8.38 

o.o5 

o.3i 

o.53 

42 
43 

34-»7 
32.84 

31-51 

1.35 
i.33 
i.33 
1.33 

86 

87 
88 

0.13 

O.2O 
0.32 

0.07 

O.I  2 

o.i  5 

131 
132 

133 

19.21 

19.49 
19.74 

0.28 

0.25 
0.23 

176 

177 
178 

7.85 

7-34 
6.83 

o.5i 
o.5i 
0.49 

44 

45 

30.18 
28.87 

t  .31 

89 
90 

0.47 
0.65 

0.18 

134 

'35 

19.97 

20.  1  8 

O.2I 

179 
1  80 

•34 
5.85 

9.49 

[20] 


TABLE  V.  —  CONTINUED. 

Perturbations  of  the  Mean  Anomaly. 

Argument  4.  —  Concluded^ 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

1  80° 

5.85 

O.47 

225° 

8.58 

o.53 

270° 

24-93 

O.II 

315° 

42.48 

0.86 

181 

5-38 

v>bf.  y 

0.45 

226 

9.II 

o.53 

271 

25.04 

O.II 

316 

43-34 

0.86 

182 

4-93 

O.43 

227 

9.64 

o.54 

272 

25.15 

O.II 

3!7 

44.20 

0.88 

183 

4.50 

O.42 

228 

IO.I8 

o.54 

273 

25.26 

O.II 

3l8 

45.08 

0.90 

184 

4.08 

O.4O 

229 

10.72 

o.54 

274 

25-37 

O.II 

3^9 

45.98 

0.90 

185 

3-68 

230 

11.26 

275 

25.48 

320 

46.88 

o.38 

o.54 

O.II 

0.92 

1  86 

3-3° 

o.35 

231 

1  1.  80 

o.54 

276 

25.59 

0.12 

321 

47.80 

0.92 

187 
1  88 

2.95 
2.62 

o.33 
o.3i 

232. 
233 

12.34 
12.87 

o.53 
o.53 

277 
278 

25.71 
25.84 

o.i3 
o.i3 

322 
323 

48.72 
49-64 

0.92 
0.93 

189 
190 

2.31 

2.02 

0.29 

234 

235 

13.40 
13.93 

o.53 

279 
280 

25-97 
26.10 

o.i3 

324 
325 

5°-57 
51.51 

0.94 

0.26 

0.52 

o.iS 

0.95 

191 

1.76 

O.23 

236 

14.45 

O.52 

281 

26.25 

o.i5 

326 

52.46 

o.o3 

192 
193 

i-53. 

O.2O 

0.18 

237 
238 

14.97 
15-47 

o.5o 
o.5o 

282 
283 

26.40 
26.57 

0.17 
0.19 

327 
328 

53-39 
54-32 

V 

0.93 
o.o3 

194 
^95 

1.15 

I.OO 

p.  1  5 

239 

240 

15-97 
16.46 

0.49 

284 

285 

26.76 
26.95 

0.19 

329 
33° 

55-25 
56.16 

7 
O.9I 

0.12 

0.48 

O.2I 

O.9I 

'  196 
197 
198 
199 

0.88 
0.79 
0.72 
0.69 

0.09 
0.07 
o.o3 

O.Ol 

241 
242 

243 
244 

16.94 

17.41 
17.87 
18.32 

0.47 
0.46 
o.45 
o.43 

286 

287 

288 
289 

27.16 
27.38 
27.62 
27.88 

O.22 

0.24 

0.26 
O.28 

333 
334 

57.07 

57-97 
58-85 
59.72 

0.90 

0.88 
0.87 

n  SA 

200 

0.68 

245 

18.75 

290 

28.16 

335 

60.58 

o.oo 

O.02 

0.42 

o.3o 

0.84 

2OI 
2O2 
203 

0.70 
0.76 
0.84 

0.06 

0.08 
O.IO 

246 
247 
248 

19.17 
19.96 

0.40 
o.3g 
o.38 

291 

292 

293 

28.46 
28.78 
29.12 

0.32 

o.34 
o.36 

336 
337 
338 

61.42 
62.23 
63.02 

0.81 
0.79 

O  tt 

204 
205 

0.94 
i.  08 

0.14 

249 

250 

20.34 
20.70 

o.36 

294 
295 

29.48 
29.86 

o.38 

339 
34° 

63-79 
64-54 

u.  /  I 

0.75 

0.16 

o.34 

0.40 

O.TI 

2O6 
207 
208 

1.24 

I-43 
1.65 

0.19 

0.22 
O.24 

251 

252 
253- 

21.04 
21.38 
21.69 

o.34 

o.3i 
0.28 

296 

297 
298 

30.26 
30.69 

0.43 
o.45 
0.48 

341 
342 
343 

65-25 
65.94 
66.59 

/ 
'0.69 

o.65 
0.62 

209 
210 

1.89 
2.16 

0.27 

254 
255 

21.97 
22.25 

0.28' 

299 
300 

31.62 
32.12 

o.5o 

344 
345 

67.21 
67.80 

o.Sg 

o.3o 

0.26 

o.53 

o.56 

21  I 
212 
213 
214 

2.46 
2.78' 
3.12 
3.48 

0.32 

o.34 
o.36 
o.3g 

256 

257 
258 
259 

22.51 
22.76 
22.99 
23.21 

0.25 
0.23 
O.22 
O.2I 

301 
302 

3°3 

304 

32.65 

33-20 
33.78 
34.38 

o.55 
o.58 
0.60 
0.62 

346 

347 
348 
349 

68.36 
68.88 

69-37 
69.81 

0.52 

0.49 
0.44 

215 

3-87 

260 

23.42 

3°5 

35.00 

35° 

70.22 

' 

0.41 

O.2O 

o.65 

o.36 

216 

2I7 

4.28 
4.70 

0.42 

261 
262 

23.62 
23.80 

0.18 

306 
3°7 

36.32 

0.67 

352 

70.58 
70.88 

o.3o 

218 

5.14 

o.44 

n  /*> 

263 

23-97 

0.17 

308 

37.02 

0.70 

353 

71.15 

0.27 

219 

22O 

5-59 
6.06 

O.4J 
0.47 

264 
265 

24.14 
24.29 

0.17 

o.i  5 

3°9 
310 

37-74 
38.48 

0.74 

354 
355 

71-37 
7L54 

0.22 
0.17 

0.49 

0.14 

0.76 

0.  12 

221 
222 
223 
224 
225 

6-55 
7.04 

7-54 
8.06 
8.58 

0.49 

o.5o 

0.52 

o.52 

266 
267 
268 
269 

270 

24-43 

24.57 
24.69 
24.81 
24-93 

0.14 

0.12 
O.I  2 
O.I  2 

312 
3*3 
3H 
315 

39.24 

40.02 

40.82 
41.64 
42.48 

0.78 
0.80 
0.82 
0.84 

356 

357 
358 

359 
360 

71.66 

71.76 
71.75 
71.69 

0.07 

o.o3 

O.OI 

0.06 

[21] 


TABLE  V.  —  CONTINUED. 

Perturbations  of  the  Mean  Anomaly. 

Argument  5. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

0° 

3-°9 

1.23 

45° 

246.47 

Q.O7 

90° 

730.36 

'35° 

1187.52 

i 

4-32 

1.45 

46 

255.54 

0.18 

9' 

74L82 

1  1  .  4-t) 
n/  / 

136 

"95-37 

7' 

2 

5-77 

1.65 

47 

264.72 

o.3o 

92 

753.26 

•44 

'37 

1203.08 

7.71 

3 
4 
5 

7.42 
9.29 
11.36 

1.87 
2.07 

48 
49 
50 

274.02 

28343 
292.96 

9-4i 

9.53 

93 
94 
95 

764.68 
776.08 
78745 

1  1  .42 

11.40 
11.37 

138 

'39 
140 

1210.64 
1218.06 
1225.34 

7-42 
7.28 

2.28 

9.64 

u.35 

7.i3 

6 

7 
8 

9 

'3-64 

I  6.  1  2 

18.81 

21.70 

2.48 
2.69 
2.89 
3.io 

53 
54 

302.60 

312.34 
322.18 

332.13 

9-74 
9-84 
9.95 

1  0.0  A 

96 

97 
98 
99 

798.80 
8  1  o.i  I 
821.37 
832.61 

n.  3i 
11.26 
11.24 

I  I     2O 

141 
142 
'43 
'44 

1232.47 
1239.44 
1246.26 
1252.93 

6.97 
6.82 
6.67 

10 

24.80 

55 

342.17 

IOO 

843.81 

'45 

1259.44 

'  l 

3.3o 

10.14 

n.  i5 

6.35 

ii 

28.10 

3.5o 

56 

352.3' 

IO  22 

101 

854.96 

146 

1265.79 

6     o 

12 

31.60 

3.70 

57 

362.53 

io.3o 

102 

866.07 

1  1  ,o5 

'47 

1271.97 

.18 

'3 
'4 
'5 

35-30 

39-'9 
43.28 

3.89 
4.09 

58 

372.83 
383.22 

393.70 

10.39 

10.48 

103 
104 

105 

877.12 
888.11 
899.06 

10.99 
10.95 

148 

'49 
150 

1277.99 
1283.85 
1289.54 

6.02 

5.86 
5.69 

4.28 

10.56 

10.89 

5.53 

16 

47.56 

4-47 

61 

404.26 

10.62 

1  06 

909.95 

10.82 

'5' 

1295.07 

A    TK 

'7 
18 

'9 

20 

52.03 
56.69 
61.54 
66.57 

4-66 
4.85 
5.o3 

62 
63 
64 
65 

414.88 
425.58 

436.34 
447.18 

10.70 
10.76 
10.84 

107 

108 
109 

IIO 

920.77 

93'-53 
942.22 
952.84 

10.76 
10.69 
10.62 

152 

'53 
'54 
'55 

1300.42 
1305.59 
1310.60 
'3  '5-43 

J.O  J 
5.17 

5.oi 

4.83 

5.22 

10.90 

10.55 

4.65 

21 

22 

7L79 
77.20 

5.4i 
5.58 

66 
67 

458.08 
469.04 

10.96 

1  1  .01 

in 

112 

963-39 
973.86 

10.47 
io.38 

156 

'57 

1320.08 
'324-55 

4-47 

23 

82.78 

5.76 

68 

480.05 

1  1.  06 

"3 

984.24 

io.3i 

158 

1328.83 

4.28 

24 

88.54 

5.94 

69 

491.11 

II    II 

114 

994-55 

'59 

1332.93 

4.10 

25 

94-48 

70 

5O2.22 

"5 

1004.78 

IO.  23 

1  60 

1336.85 

3.92 

6.  u 

11.17 

10.14 

3.73 

26 

27 
28 

100.59 
106.87 
113-32 

6.28 
6.45 
6.62 

72 
73 

5'3-39 

524.60 

535.85 

II.  21 
11.25 
1  1  .  2Q 

116 

"7 
118 

1014.92 
1024.97 
1034.92 

io.o5 
9.95 
9.86 

161 
162 
163 

1340.58 
1344.12 
'347-47 

3.54 
3.35 

29 
30 

119.94 
126.72 

6.78 

74 
75 

547.H 
558.46 

11.32 

"9 
1  20 

1044.78 
1054.54 

9.76 

164 
165 

1350.64 
'353-6i 

3.17 
2.97 

6.95 

H.36 

9.67 

o  -18 

3' 

'33-67 

1    IO 

76 

569.82 

ii.38 

121 

1064.21 

1  66 

'.356.39 

2.70 

32 

140.77- 

/•*" 
736 

77 

581.20 

1  1  .41 

122 

1073.77 

167 

'358.97 

2.58 

33 

148.03 

.^u 
1  Xf 

78 

592.61 

1  1.43 

123 

1083.22 

O*43 

168 

1361.36 

2.39 

34 

'55-44 

7.41 

79 

604.04 

1  1  .45 

124 

1092.57 

9- 

169 

1363.56 

2.20 

35 

163.01 

7-  7 

80 

615.49 

125 

1101.81 

9.24 

170 

1365.56 

2.00 

7.72 

11.47 

9-i3 

.     Q~ 

36 

170.73 

81 

626.96 

1  1.48 

126 

1110.94 

171 

y'                       /•                     1   .  OU 

1367.36         | 

37 
38 

178.59 
186.60 

8.01 
8.i5 

82 
83 

638.44 
649.92 

11.48 
1  1  .  5o 

I27 
128 

1119.94 
1128.83 

9.00 
8.89 

ft    -if, 

172 
'73 

1368.96 
1370.36 

1.  6O 

I.4O 

39 

194.75 

8  20 

84 

661.42 

i  i.5o 

I29 

"37.59 

O.j\J 
ft   f\^ 

'74 

1371.56 

I.  2O 

4° 

203.04 

0.49 

85 

672.92 

I3O 

1  146.24 

O.UJ 

'75 

1372.56 

I.OO 

8.43 

n.  5o 

8.52 

o 

4' 

211.47 

8.55 

86 

684.42 

'3' 

1154.76 

8     In 

176 

I373-36 

O.  oO 

42 

220.02 

8.69 

87 

695.92 

1  1  .00 
1  1.48 

132 

1163.15 

.09 

Q  9« 

177 

'373-95 

o.  39 

43 

228.71 

8.82 

88 

707.40 

11.48 

'33 

1171.40 

OfftJ 

8.i3 

178 

'374-34 

0.18 

44 
45 

237-53 
246.47 

8.94 

89 
90  i 

718.88 
730.36 

11.48 

'34 
'35 

"79-53 
1187.52 

7-99 

179 
1  80 

'374-52 
'374-5' 

O.OI 

[22] 


TABLE   V.  —  CONTINUED. 

Perturbations  of  the  Mean  Anomaly. 

Argument  5.  —  Concludrdr 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq.           D. 

1  80° 

I374-5I 

225° 

1165.63 

8.89 

270° 

658.84 

315° 

l67-I9     8o4 

181 

1374.28 

0.  2o 

0.43 

226 

1156.74 

9.o3 

271 

646.37 

12.47 
12.45 

316 

'59-'5  7;85 

182 

'83 
184* 

1373.85 
1373.21 
1372.36 

0.64 

o.85 

227 
228 
229 

1147.71 
1138.52 
1129.19 

9.19 
9.33 

272 
273 
274 

633.92 
621.49 
609.08 

12.43 
12.41 

317 
318 

3'9 

151.30 
143.62 
136.12 

7.68 
7-5o 

1  32 

185 

I37I-3I 

1  .00 

230 

1119.70 

9.49 

275 

596.68 

12.40 

320 

128.80 

7«*> 

1.26 

9.63 

12.37 

7.i3 

1  86 
187 
188 

1370.05 
1368.59 
1366.92 

1.46 

1.67 

1.88 

231 
232 

233 

IIIO.O7 
1100.30 
1090.40 

9-77 
9.90 

276 

277 
278 

584.31 
571.98 

559^9 

I 

12.33 
12.29 

321 
322 
323 

121.67 
114.72 
107.96 

6.95 
6.76 
6.56 

189 

1365.04 

2.08 

234 

1080.36 

10.04 
10.18 

279 

547-44 

12.25 
12  21 

324 

101.40 

6.38 

190 

1362.96 

235 

1070.18 

280 

535.23 

325 

95.02 

2.29 

io.3o 

12.  l6 

6.18 

191 
192 
^93 

1360.67 

1358.17 
1355.46 

2.5o 

2.71 

Q  n  I 

236 

237 
238 

1059.88 
1049.45 
1038.91 

10.43 
10.54 

281 
282 
283 

523.07. 
510.97 
498.92 

12.10- 
12.05 

n_Q 

326 

327 
328 

88.84 
82.86 
77.07 

5.98 
5.79 
5.58 

194 
»95 

1352.55 

1  3  49-44 

^.91 

3.  ii 

239 
240 

1028.24 
1017.46 

I  O.O*7 

10.78 

284 
285 

486.94 
475.02 

.Qo 
11.92 

329 
33°- 

7L49 
66.  i  o 

5.39 

3.32 

10.90 

u.85 

5.i8 

196 

1346.12 

3.52 

241 

1006.56 

1  1.  00 

286 

463.17 

1  1  11 

33i 

60.92 

4-97 

197 

1342.60 

3  T2 

242 

995.56 

287 

451.40 

1  *•  /  / 

332 

55-95 

A  11 

198 
199 

1338.88 
1  3  34.96 

0.7^ 
3.92 
4.  i3 

243 
244 

98445 
973.24 

11*11 

II.  21 

li.3i 

288 
289 

439-70 
428.09 

1  1  .70 
n.  61 

Tf     K-l 

333 
334 

51.18 
46.62 

4-77 
4.56 
4.35 

2DO 

1330-83 

245 

961.93 

290 

416.56 

11.  JO 

335 

42.27 

4.33 

11.41 

11.44 

4-14 

201 

1326.50 

4.53 

246 

950.52 

n.4o 

291 

405.12 

ii.34 

336 

38.13 

3.94 

2O2 
203 

1321.97 
1317.24 

4.73 
4.93 

247 
248 

939-03 
927.46 

^7 

11.57 

u.66 

292 
293 

393.78 
382.55 

11.23 

11.14 

337 
338 

34-19 
30.47 

3.72 
3.5o 

204 

1312.31 

5.i3 

249 

915.80 

294 

37I-41 

339 

26.97 

3.3o 

205 

1307.18 

250 

904.06 

11.74 

295 

360.37 

11.04 

340 

23.67 

5.32 

11.82 

10.93 

3.o8 

2O6 

1301.86 

5.52 

251 

892.24 

1  1  88 

296 

349-44 

10.81 

34i 

20.59 

2.86 

207 
208 
209 

1296.34 
1290.63 
1284.73 

5.7i 
5.90 
6.00 

252 

253 
254 

880.36 
868.41 
856.39 

1  1  .00 
11.95 

12.02 

1  2.  08 

297 
298 

299 

338.63 
327-94 
317.36 

10.69 
10.58 

IO.46 

342" 
343 
344 

17.73 
15.08 
12.64 

2.65 

2.44 

2.22 

2IO 

1278.64 

255 

844.3I 

300 

306.90 

345 

10.42 

6.28* 

12.  l3 

io.33 

2.00 

21  I 
212 

1272.36 
1265.89 

6.47 
6.65 

256 

257 

832.18 
820.00 

12.  l8 
12.23 

301 
302 

296.57 
286.38 

10.19 
1  0.06 

346 

347 

8.42 
6.63 

1-79 

i  5i 

2I3 

1259.24 

6.84 

258 

807.77 

12.27 

303 

276.32 

9.93 

348 

5.06 

i  .  ^  i 
i.36 

214 

1252.40 

7n9 

259 

795-50 

/ 
r  o   T  i 

3°4 

266.39 

349 

3-70 

I  IA 

2I5 

I245-38 

.OJ 

260 

78^.19 

1  4.3  I 

3°5 

256.60 

9-79 

350 

2.56 

i.i^ 

7-20 

12.35 

9.64 

0.92 

216 

1238.18 

7.38 

261 

770.84 

12.38 

306 

246.96 

35i 

1.64 

O.TO 

217 

218 

219 

22O 

1230.80 
1223.25 
1215.52 
1207.62 

7.55 
7.73 
7.90 

262 
263 
264 
265 

758.46 
746.06 

733.63 
72I.I8  ' 

12.40 
12.43 
12.45 

3°7 
308 

3°9 
310 

237.46 
228.12 
218.94 
209.90 

Q.  DO 

9.34 
9.18 
9.04 

352 
353 
354 
355 

0-94 
0-45 
o.i  8 
0.13 

0.49 
0.27 
O.OD 

8.07 

12.46 

8.87 

0.16 

221 

1199.55 

o  0? 

266 

708.72 

311 

201.03 

fi     -!¥ 

356 

0.29 

r>    38 

222 
223 
224 
225 

1 

1191.32 
1182.92 
1174.36 
1165.63 

O.  4-J 

8.40 
8.56 
8.73 

267 
268 
269 

270 

696.25 
683.78 
671.31 
658.84 

12.47 
12.47 
12.47 
12.47 

312 
3'3 
3H 
3i5 

192.32 
183.78 
175.40 
167.19 

8.71 

8.54 
8.38 

8.21 

357 
358 

359 
360 

0.67 
1.27 
2.07 
3-09 

O.OO 
O.60 
0.80 

1.02 

[23] 


TABLE  V.  —  CONTINUED. 

Perturbations  of  the  Mean  Anomaly. 

Argument  6.                                                                   Argument  7. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

0° 

21.94 

0.45 

1  80° 

26.40 

o.36 

0° 

36.58 

o.i5 

I  80° 

2.22 

o.i5 

5 

19.68 

0.45 

185 

28.18 

o.35 

5 

35-75 

0.18 

185 

3-05 

0.18 

10 

17.46 

0.44 

190 

29.94 

o.35 

10 

34.80 

0.20 

190 

4.OO 

O.2O 

15 

15.29 

0.42 

195 

3'-64 

o.34 

15 

33-73 

0.22 

»95 

5.07 

0.22 

20 

13.21 

0.41 

200 

33-31 

o.33 

20 

32.56 

0.25 

2OO 

6.24 

*0.25 

25 

11.22 

0.89 

205 

34-92 

0.32 

25 

31.28 

0.27 

•    205 

7.52 

0.27 

30 

9-35 

o.36 

2IO 

36-47 

o.3o 

30 

29.90 

0.28 

2IO 

8.90 

0.28 

35 

7.62 

o.33 

215 

37-95 

0.29 

35 

28.46 

o.3o 

215 

10.34 

o.3o 

40 

6.04 

o.3o 

220 

39-36 

0.27 

40 

26.94 

o.3i 

22O 

11.86 

o.3i 

45 

4.64 

0.26 

225 

40.67 

0.25 

45 

25.36 

0.32 

225 

13-44 

0.32 

5° 

3-39 

0.23 

230 

41.89 

0.23 

50 

23-74 

o.33 

230 

15.06 

0.33 

55 

2-34 

0.19 

235 

43-01 

0.21 

55 

22.08 

o.33 

235 

16.72 

o.33 

60 

1.49 

o.i5 

240 

44.01 

0.19 

60 

20.41 

o.33 

240 

18.39 

o.33 

65 

0.84 

O.I  I 

245 

44.88 

0.16 

65 

18.73 

0.33 

245 

20.07 

o.33 

70 

0.38 

0.07 

250 

45.62 

o.i3 

70 

17.06 

0.33 

250 

21.74 

o.33 

75 

0.14 

o.o3 

255 

46.23 

O.IO 

75 

15.40 

o.33 

255 

23.40 

o.33 

80 

0.09 

O.OI 

260 

46.67 

0.07 

80 

13.76 

0.32 

260 

25.04 

0.32 

85 

0.24 

o.o5 

265 

46.96 

0.04 

85 

12.18 

o.3i 

265 

26.62 

o.3i 

90 

0.57 

0.09 

270 

47.09 

O.OI 

90 

10.65 

o.3o 

270 

28.15 

o.3o 

95 

1.  10 

0.12 

275 

47.04 

o.o3 

95 

9.19 

0.28 

275 

29.61 

0.28 

IOO 

1.79 

o.i5 

280 

46.81 

0.06 

IOO 

7.80 

0.27 

280 

31.00 

0.27 

105 

2.65 

0.18 

285 

46.41 

O.IO 

105 

6.50 

O.25 

285 

32-3° 

O.25 

no 

3-64 

O.2I 

290 

45.84 

o.i3 

no 

5-30 

0.23 

290 

33-5° 

0.23 

"5 

4-79 

0.24 

295 

45.06 

0.17 

"5 

4.21 

0.21 

295 

34-59 

0.21 

120 

6.07 

0.26 

3OO 

44.11 

0.21 

1  20 

3.23 

0.18 

300 

35-57 

0.18 

125 

744 

0.28 

305 

42.99 

0.24 

125 

2.39 

0.16 

3°5 

36.41 

0.16 

130 

8.91 

o.3o  . 

310 

41.69 

0.28 

130 

1.66 

o.i3 

310 

37-H 

o.i3 

»35 

10.48 

o.3i 

315 

40.22 

o.3i 

135 

1.07 

O.IO 

3^5 

37-73 

O.IO 

140 

12.12 

.  o.33 

320 

38.60 

o.34 

140 

0.62 

0.08 

320 

3'8.i8 

0.08 

»45 

13.82 

o.34 

325 

36.84 

o.36 

H5 

0.31 

o.o5 

325 

38.49 

o.o5  . 

150 

15.56 

0.35 

330 

34-95 

0.39 

150 

0.14 

O.02 

33° 

38.66 

O.O2 

»55 

17-34 

o.36 

335 

32.95 

0.41 

155 

0.13 

O.OI 

.  335 

38.67 

O.OI 

1  60 

19.15 

o.36 

34° 

30.85 

o.43 

1  60 

0.26 

0.04 

34° 

38.54 

O.O4 

165 

20.97 

o.36 

345 

28.68 

0.44 

165 

0.54 

0.07 

345 

38-26 

0.07 

170 

22.78 

o.36 

35° 

26.46 

0.45 

170 

0.96 

O.IO 

35° 

37-84 

O.IO 

»75 

24.60 

o.36 

355 

24.21 

0.45 

175 

1.52 

o.i3 

355 

37.28 

o.i3 

1  80 

26.40 

o.36 

360 

21.94 

o.45 

1  80 

2.22 

o.  i5 

360 

36.58 

o.i5 

V 

*!t*  The  Differences  are  calculated  for  i   Degree. 

[24] 


TABLE  V.  —  CONTINUED. 

Perturbations  of  the  Mean  Anomaly. 

Argument  8.                                                                   Argument  9. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

0° 

0.14 

o.o3 

1  80° 

28.46 

o.o3 

0° 

3.89 

0.16 

1  80° 

2347 

0.16 

5 

0-35 

o.o5 

I85 

28.25 

o.o5 

5 

3.12 

o.i5 

185 

24.22 

o.  14 

10 

0.66 

0.07 

190 

27.94 

0.07 

10 

2.42 

o.i3 

190 

24.90 

0.12 

•'5 

i.  08 

0.09 

195 

27.52 

0.09 

15 

1.79 

0.12 

195 

2547 

O.II 

20 

i.  60 

O.II 

2OO 

27.00 

O.II 

20 

1.24 

O.IO 

200 

25.96 

O.Og 

25 

2.21 

o.i3 

205 

26.39 

o.i  3 

25 

0.80 

0.08 

205 

26.35 

0.07 

3° 

2.92 

o.i5 

210 

25.68 

o.i  5 

3° 

0.47 

0.06 

2IO 

26.65 

o.o5 

35 

3-72 

0.17 

2I5 

24.88 

0.17 

35 

O.22 

0.04 

215 

26.84 

o.o3 

40 

4.60 

0.18 

22O 

24.00 

0.18 

40 

0.07 

O.02 

22O 

26.93 

O.OI 

45 

5-55 

0.19 

225 

23.04 

0.19 

45 

0.03 

O.OO 

•    225 

26.92 

O.O2 

5° 

6-57 

0.21 

230 

22.03 

0.21 

5° 

O.IO 

O.O2 

230 

26.82 

o.o3 

55 

7.65 

0.22 

235 

20.96 

0.22 

55 

0.27 

0.04 

235 

26.61 

o.o5 

60 

8-77 

0.23 

240 

19.83 

0.23 

60 

°-54 

0.06 

240 

26.30 

0.07 

65 

9-94 

0.24 

245 

18.66 

0.24 

65 

0.91 

0.08 

245 

25.90 

0.09 

70 

1  1.14 

0.24 

250 

17.46 

0.24 

70 

1.38 

O.IO 

250 

25.42 

O.II 

75 

12.36 

0.25 

255 

16.24 

0.25 

75 

1.94 

O.I  2 

255 

24.84 

o.i3 

So 

13.60 

0.25 

260 

15.00 

0.25 

80 

2.61 

0.14 

260 

24.19 

0.14 

85 

14.85 

0.25 

265 

13.75 

0.25 

85 

3.36 

o.  16 

265 

23.46 

o.i  5 

90 

16.09 

0.25 

270 

12.51 

0.25 

90 

4.19 

0.17 

270 

22.65 

0.17 

95 

17-31 

0.24 

275 

11.29 

0.24 

95 

5.09 

0.19 

275 

21.77 

0.18 

IOO 

18.52 

0.24 

280 

I  O.08 

0.24 

IOO 

6.05 

O.2O 

280 

20.83 

0.19 

105 

19.69 

0.23 

285 

8.91 

0.23 

105 

7.09 

0.21 

285 

19.84 

0.20 

I  IO 

20.82 

O.22 

290 

7.78 

0.22 

no 

8.18 

0.22 

290 

18.82 

O.2I 

H5 

21.90 

0.21 

295 

6.69 

O.2I 

"5 

9.31 

0.23 

295 

1775 

0.21 

1  20 

22.93 

O.2O 

3OO 

5.67 

0.20 

1  20 

10.45 

0.23 

3OO 

16.64 

O.22 

125 

23.88 

O.lg 

3°5 

4.72 

0.19 

125 

1  1.62 

0.24 

305 

'5-52 

0.22 

130 

24.77 

0.17 

310 

3.83 

O.I7 

130 

12.82 

0.24 

310 

H.38 

0.23 

135 

25-57 

o.i5 

3^5 

3.02 

.  o.i5 

135 

14.01 

0.24 

315 

13.22 

0.23 

140 

26.30 

o.i3 

32O 

2.30 

o.i  3 

140 

15.21 

O.24 

320 

12.07 

0.23 

145 

26.92 

0.12 

325 

1.67 

0.12 

H5 

16.39 

0.23 

325' 

10.93 

0.23 

.  150 

27.46 

O.  IO 

33° 

I.I4 

0.10 

150 

17.55 

0.22 

330 

9.81 

0.22 

155 

27.89 

0.08 

335 

0.7I 

0.08 

155 

18.67 

O.2I 

335 

8.71 

0.21 

1  60 

28.22 

O.06 

34° 

0.38 

O.o6 

1  60 

'9-74 

O.20 

34° 

7.66 

O.2I 

165 

28.44 

0.04 

345 

o.i  6 

O.04 

165 

20.74 

0.19 

345 

6.64 

0.2O 

170 

28.56 

0.02 

35° 

0.04 

OJ02 

170 

21.70 

O.lg 

35° 

5.66 

0.19 

175 

28.56 

o.oo 

355 

0.04 

O.OO 

»75 

22.61 

•  0.18 

355 

4-74 

'0.18 

1  80 

28.46 

o.o3 

360 

0.14 

o.o3 

1  80 

23-47 

0.17 

360 

3.89 

O.l6 

* 

%.*The  Differences  -are  calculated  for  i   Degree. 

[25] 


TABLE  V.  —  CONTINUED. 

Perturbations  of  the  Mean  Anomaly. 

Argument  10.                                                        Argument  IT. 

Arg.< 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

0° 

'5-41 

0.21 

1  80° 

11.51 

0.22 

0° 

3-91 

0.14 

180° 

16.83 

0.14 

5 

16.41 

O.20 

185 

10.45 

O.2I 

5 

3-25 

o.i3 

185 

17.49 

0.12 

10 

17.37 

O.IQ 

190 

9.39 

0.21 

10 

2.63 

O.I2 

190 

18.09 

O.II 

'5 

18.29 

0.18 

195 

8-35 

O.2I 

15 

2.07 

O.II 

'95 

18.63 

O.IO 

20 

19.17 

0.17 

200 

7-33 

0.20 

20 

1.57 

0.09 

200 

19.1  1 

0.09 

25 

19.98 

0.16 

205 

6-34 

O.lg 

25 

1.14 

0.08 

205 

19.51 

0.07 

3° 

20.74 

o.i5 

2IO 

5.40 

0.18 

3° 

0.78 

0.07 

2IO 

19.84 

O.O6 

35 

21.42 

0.14 

215 

4-51 

0.17 

35 

0.48 

0.06 

215 

20.1  I 

o.o5 

40 

22.04 

0.12 

220 

3.68 

0.16 

40 

0.27 

0.04 

22O 

2O.3I 

o.o3 

45 

22.58 

0.10 

225 

2.91 

0.14 

45 

0.13 

0.02 

225 

20.42 

O.OI 

5° 

23.07 

0.09 

230 

2.23 

o.i3 

5° 

0.08 

O.OI 

230 

20.46 

o.oo 

55 

23-49 

0.08 

235 

1.64 

O.II 

55 

0.09 

O.OI 

235 

20.43 

O.OI 

60 

23.84 

O.O6 

240 

1.14 

0.09 

60 

0.19 

o.o3 

240 

2O.32 

o.o3 

65 

24.11 

o.o5 

245 

0.71 

0.07 

65 

0-37 

0.04 

245 

20.13 

o.o5 

70 

24.31 

o.o3 

250 

0-39 

o.o5 

70 

0.62 

0.06 

250 

19.86 

0.06 

75 

2443 

0.02 

255 

0.19 

o.o3 

75 

0.95 

0.07 

255 

19.51 

0.08 

80 

24.47 

o.oo 

260 

0.09 

O.OI 

80 

1-34 

0.09 

260 

19.10 

0.09 

85 

24.45 

0.01 

265 

0.09 

O.OI 

85 

1.81 

O.IO 

265 

18.63 

O.IO 

90 

24.36 

o.o3 

270 

O.20 

o.o3 

90 

2-35 

O.II 

270 

i8.n 

O.II 

95 

24.20 

0.04 

275 

0-43 

0.06 

95 

2.94 

o.i3 

275 

17.52 

"  o.i  a 

IOO 

23.96 

0.06 

280 

0.76 

0.08 

IOO 

3.60 

0.14 

280 

16.88 

o.i3 

105 

23.64 

0.07 

285 

1.20 

O.IO 

105 

4.3i 

o.i  5 

285 

16.19 

0.14 

no 

23.24 

0.09 

290 

i-74 

•O.II 

IIO 

5.06 

o.i  5 

290 

15.46 

o.i5 

"5 

22.77 

0.10 

295 

2.40 

o.i3 

"5 

5.86 

0.16 

295 

14.70 

0.16 

1  20 

22.24 

O.I  I 

300 

3.10 

o.i5 

1  20 

•   6.69 

0.17  ' 

3OO 

13.89 

0.17 

125 

21.63 

o.i3 

3°5 

3-9i 

0.17 

125 

7-54 

0.17 

305 

13>°S 

0.17 

130 

20.96 

0.14 

310 

4.80 

0.18 

130 

8.42 

0.18 

3IO 

12.20 

0.17 

'35 

20.22 

o.i5 

3i5 

5-74 

0.19 

135 

9.3i 

0.18 

315 

"•33 

0.17 

140 

f943 

0.16 

320 

6-75 

0.20 

140 

IO.2I 

0.18 

32O 

10.45 

0.18 

H5 

18.58 

0.18 

325 

1-11 

0.21 

H5 

11.  1  I 

0.18 

325 

9-57 

0.18 

150 

17.67 

0.19 

330 

8.83 

0.22 

150 

I2.OO 

0.18 

33° 

8.70 

0.17   - 

155 

16.72 

0.19 

335 

9-93 

0.22 

155 

12.87 

0.17 

335 

7.83 

0.17 

1  60 

15-73 

0.20 

34° 

11.05 

0.22 

1  60 

'3-73 

0.17 

34° 

6.99 

0.17 

165 

14.71 

0.21 

345 

12.  16 

0.22 

165 

14-57 

0.16 

345 

6.18 

o.  16 

170 

13.67 

O.2I 

35° 

13-25 

0.22 

170 

15-37 

o.i5 

35° 

5-39 

o.i  5 

»75 

I  2.6  1 

O.22 

355 

H-35 

0.22 

»75 

1  6.  1  2 

o.  i5 

355 

4-63 

o.i5 

1  80 

11.51 

0.22 

360 

15.41 

0.21 

1  80 

16.83 

o.i  4 

360 

3-91 

0.14 

%*  The  Differences  are  calculated  for  i  Degree. 

[26] 


TABLE  V.—  CONTINUED. 

Perturbations  of  the  Mean  Anomaly. 

Argument  12.                                                           Argument  13. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

0° 

2.32 

O.IO 

1  80° 

15.18 

O.IO 

0° 

0.30 

0.04 

1  80° 

17.50 

0.04 

5 

2.84 

O.I  I 

185 

14.65 

O.I  I 

5 

o-53 

o.o5 

185 

17.27 

o.o5 

10 

3-42 

0.12 

190 

14.08 

0.12 

10 

0.82 

0.06 

190 

16.98 

0.07 

15 

4-°3 

o.i3 

'95 

'13-47 

o.i3 

15 

1.18 

0.08 

'95 

16.62 

0.08 

20 

4.68 

o.i3 

200 

12.82 

o.i3 

20 

1.59 

0.09 

200 

16.21 

0.09 

25 

5-36 

0.14 

205 

12.15 

0.14 

25 

2.06 

O.IO 

205 

15.74 

O.IO 

3° 

6.07 

0.14 

2IO 

"•43 

0.14 

30 

2-57 

O.I  I 

2IO 

15.23 

O.I  I 

35 

6.79 

o.i5 

2I5 

10.71 

o.i5 

35 

3-H 

O.I2 

2I5 

14.65 

0.12 

40 

7-53 

o.i5 

22O 

9-97 

o.i5 

40 

3-75 

o.i3 

22O 

14.05 

o.i  3 

45 

8.28 

o.i  5 

225 

9.21 

o.i5 

45 

4.40 

o.i3 

225 

J3-39 

o.i3 

5° 

9.04 

o.i5 

230 

8.46 

o.i  5 

50 

5.08 

0.14 

230 

12.72 

0.14 

55 

9-79 

o.i  5 

235 

7.71 

o.i5 

55 

5-79 

o.i5 

235 

12.00 

0.14 

60 

10.54 

o.i5 

240 

6.96 

o.i5 

60 

6.53 

o.i5 

240 

11.27 

o.i5 

65 

11.26 

0.14 

245 

6.23 

0.14 

65 

7.28 

o.i5 

245 

IO.5I 

o.i5 

70 

11.97 

0.14 

250 

5-53 

0.14 

70 

8.06 

o.i5 

250 

9-74 

o.i  5 

75 

12.65 

o.i3 

255 

4.85 

o.i  3 

75 

8.83 

o.i5 

255 

8.96 

0.1  5 

80 

i3-3i 

o.i3 

260 

4.19 

o.i3 

80 

9.61 

o.i5 

260 

8.19 

o.i5 

85 

13-93 

0.12 

265 

3-56 

O.I  2 

85 

10.37 

o.i  5 

265 

7-43 

o.i5 

90 

14.52 

O.Il 

270 

2.98 

O.I  I 

90 

11.13 

o.i5 

270 

6.67 

o.i5 

95 

15.06 

O.IO 

275 

2.44 

O.IO 

95 

11.87 

o.i5 

275 

5-93 

o.i5 

IOO 

15-55 

0.09 

280 

1.95 

0.09 

IOO 

12.59 

0.14 

280 

5-2i 

0.14 

105 

15.98 

0.08 

285 

1.52 

0.08 

105 

13-28 

o.i3 

285 

4.51 

0.14 

no 

16.37 

0.07 

290 

i.«3 

0.07 

no 

13-94 

o.i3 

290 

3.86 

o.i3 

"5 

16.70 

0.06 

295 

0.80 

0.06 

"5 

H-55 

0.  12 

295 

3-24 

0.12 

1  20 

16.96 

o.o5 

30O 

0.54 

o.o5 

120 

15.  '3 

O.I  I 

300 

2.67 

O.I  I 

125 

17.16 

o.o3 

3°5 

0-34 

o.o3 

125 

15.66 

O.IO 

305 

2.14 

O.IO 

130 

17.30 

O.O2 

310 

O.2O 

0.02 

130 

16.14 

0.09 

310 

1.66 

0.09 

'35 

17-37 

O.OI 

3i5 

O.I  2 

O.OI 

135 

16.56 

0.08 

315 

1.23 

0.08 

140 

17-39 

O.OI 

320 

O.I  I 

O.OI 

140 

16.93 

0.07 

32O 

0.87 

0.07 

»45 

17.33 

0.02 

325 

0.17 

O.02 

H5 

17.23 

o.o5 

325 

0.57 

o.o5 

150 

17.21 

o.o3 

33° 

0.29 

o.o3 

150 

17.47 

0.04 

33° 

0-33 

0.04 

'55 

17.01 

0.04 

335 

0.48 

0.04 

155 

17.64 

o.o3 

335 

0.16 

o.o3 

1  60 

16.76 

0.06 

34° 

0.74 

0.06 

1  60 

17-75 

O.OI 

34° 

0.05 

O.OI 

165 

16.45 

0.07 

345 

1.05 

0.07 

165 

17.79 

o.oo 

345 

O.OI 

o.oo 

170 

1  6.08 

0.08 

350 

1.42 

p.o8 

170 

17.76 

O.OI 

35° 

0.04 

O.OI 

175 

15.65 

0.09 

355 

1.84 

o  09 

175 

17.66 

o.o3 

355 

0.14 

o.o3 

1  80 

15.18 

O.IO 

360 

2.32 

O.IO 

1  80 

17.50 

0.04 

360 

0.30 

0.04 

%*  The  Differences  are  calculated  for  i  Degree. 

[27] 


TABLE  V.  —  CONTINUED. 

Perturbations  of  the  Mean  Anomaly. 

Argument  14.                                                          Argument  15. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

0° 

18.55 

0.09 

180° 

i-43 

0.09 

0° 

12.47 

0.06 

180° 

0.07 

0.00 

5 

18.96 

0.08 

185 

i.  02 

0.08 

5 

12.13 

0.07 

185 

O.IO 

O.OI 

10 

19.30 

0.06 

190 

0.68 

0.06 

10 

11.79 

0.07 

190 

0.21 

o.o3 

15 

19-57 

o.o5 

*95 

0.41 

o.o5 

'5 

"•43 

0.07 

195 

°-39 

o.o5 

20 

19.77 

o.o3 

200 

O.2I 

o.o3 

20 

1  1.  08 

0.07 

200 

0.66 

0.06 

25 

19.89 

O.OI 

205 

0.08 

O.O2 

25 

10.72 

0.07 

205 

I.OO 

0.07 

30 

19.94 

0.00 

2IO 

0.04 

0.00 

3° 

10.37 

0.07 

2IO 

1.41 

0.09 

35 

19.91 

O.OI 

215 

0.07 

O.OI 

35 

10.01 

0.07 

215 

1.90 

O.IO 

40 

19.80 

o.o3 

22O 

0.18 

o.o3 

40 

9.65 

0.07 

220 

2.45 

O.I  2 

45 

19.62 

0.04 

225 

0.36 

0.04 

45 

9.29 

0.07 

225 

3-°7 

o.i3 

5° 

19-37 

o.o5 

230 

0.61 

o.o5 

5° 

8.93 

0.07 

230 

3-73 

0.14 

55 

19.05 

0.07 

235 

°-93 

0.07 

55 

8.59 

0.07 

235 

4-43 

o.i5 

60 

18.66 

0.08  - 

240 

1.32 

0.08 

60 

8.25 

0.07 

240 

5-17 

o".i5 

65 

18.20 

0.09 

245 

1.78 

0.09 

65 

7.91 

0.07 

245 

5-94 

0.16 

70 

17.68 

O.II 

250 

2.30 

0.11 

70 

7-57 

0.07 

250 

6.73 

0.16 

75 

17.09 

0.12 

255 

2.89 

0.12 

75 

7.21 

0.07 

255 

7-5  i 

o.i5 

80 

16.46 

o.i3 

260 

3-52 

o.i3 

80 

6.85 

0.07 

260 

8.27 

o.i5 

85 

15.77 

0.14 

265 

4.20 

0.14 

85 

6.49 

0.07 

265 

9-°3 

o.i  5 

90 

15.05 

o.i  5 

270 

4-93 

o.i5 

90 

6.12 

0.08 

270 

9-74 

o.  14 

95 

14.28 

0.16 

275 

5.70 

0.16 

95 

5-73 

0.08 

275 

10.43 

o.i3 

100 

'3-49 

0.16 

280 

6.49 

0.16 

100 

5-33 

0.08 

280 

11.07 

O.I  2 

105 

12.66 

0.17 

285 

7-31 

0.17 

105 

4.92 

0.08 

285 

1  1.64 

O.II 

no 

11.82 

0.17 

290 

8.16 

0.17 

no 

4.51 

0.08 

290 

12.15 

0.09 

115 

10.95 

0.17 

295 

9.02 

0.17 

i'5 

4.08 

0.09 

295 

12.59 

0.08 

1  20 

10.09 

0.17 

3OO 

9.89 

0.17 

120 

3-65 

0.09 

300 

12.97 

0.07 

125 

9-23 

0.17 

305 

10.75 

0.17 

125 

3.22 

0.09 

305 

13.27 

0.06 

130 

8-37 

0.17 

310 

1  1.  6  1 

0.17 

130 

2.79 

0.08 

310 

i3-5i 

0.04 

135 

7.52 

0.17 

315 

12.46 

0.17 

135 

2-37 

0.08 

315 

13.67 

o.o3 

140 

6.69 

0.16 

32O 

13.29 

0.16 

140 

1.97 

0.08 

32O 

13-77 

O.OI 

H5 

5-89 

0.16 

325 

14.09 

0.16 

H5 

1.59 

0.07 

325 

'3-79 

0.00 

150 

5.11 

o.i  5 

33° 

14.87 

o.i5 

150 

1.23 

0.07 

33° 

13-75 

O.OI 

'55 

4-37 

0.14 

335 

15.60 

o.  14 

155 

0.90 

0.06 

335 

13.64 

o.o3 

1  60 

3.68 

o.i3 

34° 

16.30 

o.i3 

1  60 

0.62 

o.o5 

34° 

13.48 

0.04 

165 

3-04 

0.  12 

345 

16.94 

O.I  2 

I65 

o-39 

0.04 

345 

13.29 

0.04 

170 

2-44 

O.II 

35° 

»7-54 

O.II 

170 

0.23 

o.o3 

35° 

13-0$ 

o.o5 

'75 

1.90 

O.IO 

355 

18.07 

O.IO 

»75 

O.I  2 

O.O2 

355 

12.78 

0.06 

1  80 

i-43 

0.09 

360 

18.55 

0.09 

ISO 

O.O7 

O.'QO 

360 

12.47 

0.06 

*$•*  The  Differences  are  calculated  for  i  Degree. 

[28] 


TABLE  V.—  CONTINUED. 

Perturbations  of  the  Mean  Anomaly. 

Argument  16.                                                           Argument  17. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

0° 

9.69 

O.  IO 

1  80° 

5-77 

o.o3 

0° 

2.41 

0.08 

1  80° 

1.64 

o.o4 

5 

10.14 

0.08 

185 

5.61 

o.o4 

5 

2.OI 

0.08 

185 

1.85 

Q.Q4 

10 

10.54 

0.07 

190 

5.41 

o.o5 

10 

1.65 

0.07 

190 

2.07 

o.o4 

15 

10.83 

o.o5 

195 

5-'5 

0.06 

15 

i-34 

0.06 

'95 

2.30 

o.o5 

20 

11.03 

o.o3 

2OO 

4.85 

'0.06 

20 

1.08 

o.o,5 

2OO 

2.55 

o.o5 

25 

1  1.14 

O.OI 

205 

4.50 

o.o5 

25 

0.86 

0.04 

205 

2.81 

o.q5 

30 

1  1  .  j  6 

O.OI 

210 

4.11 

0.08 

3° 

0.69 

o.o3 

2IO 

3.20 

0.06 

35 

11.09 

O.O2 

215 

3-69 

0.09 

35 

0.55 

O.02 

215 

3-31 

0.07 

40 

10.95 

0.04 

22O 

3-25 

0.09 

40 

0.44 

O.Q2 

22O 

3-75 

Q.Q7 

45 

10.73 

o.o5 

225 

2.79 

Q.Q9 

45 

0.36 

o.oi 

225 

4.10 

0.97 

5° 

10.46 

0.06 

230 

2.33 

Q.Q9 

5° 

0.31 

O.OI 

230 

4-47 

O.o8 

55 

10.12 

0.07 

235 

1.88 

q.09 

55 

0.26 

O.OI 

235 

4.86 

0.08 

60 

9-75 

0.08 

240 

'•45 

0.08 

60 

O.22 

O.OI 

240 

5.26 

O.o8 

65 

9-35 

0.08 

245 

1.  06 

0.07 

65 

O.I9 

O.OI 

245 

5.66 

0.08 

70 

8.94 

0.08 

250 

0.72 

0.06 

70 

o.i  6 

O.OI 

250 

6.05 

O.o8 

75 

8.52 

0.08 

255 

°-43 

o.o5 

75 

0.13 

o.oo 

255 

6-43 

0.07 

80 

8.10 

0.08 

260 

0.21 

o.o3 

80 

O.II 

o.oo 

260 

6.79 

O.07 

85 

7.70 

0.08 

265 

0.07 

O.Q2 

85 

0.08 

O.OI 

265 

7.10 

O.q6 

90 

7-33 

0.07 

270 

O.OI 

O.QO 

90 

0.05 

0.0^0 

270 

7.38 

o.o5 

95 

6.99 

0.06 

275 

0.04 

O.OI 

95 

0.03 

0.00 

275 

7.59 

o.o4 

IOO 

6.69 

o.o5 

280 

0.1-6 

9-o3 

IOO 

O.OI 

o.oo 

280 

7-75 

O.Q2 

105 

6.44 

0.04 

285 

0.38 

o.o5 

105 

o.oo 

O.QO 

285 

7.83 

O.OI 

no 

6.23 

o.o3 

290 

0.69 

0.07 

no 

o.oo 

O.QO 

290 

7.85 

O.OI 

H5 

6.07 

O.O2 

295 

1.09 

0.09 

"5 

O.OI 

o.oo 

295 

7.78 

O.O2 

120 

5.96 

O.O2 

300 

i-57 

Q.IQ 

1  20 

0.05 

O.OI 

300 

7.64 

o.o3 

125 

5.88 

O.OI 

305 

2.13 

0.12 

125 

O.IO 

O.QI 

3°5 

7.41 

o.o5 

I30 

5.85 

o.oo 

310 

2.75 

O.l3 

130 

0.17 

O.OI 

310 

7.12 

0.07 

135 

5.84 

o.oo 

315 

3-43 

Q.I4 

135 

0.25 

0.02 

315 

6.76 

0.08 

140 

5.86 

o.oo 

320 

4.15 

o.i5 

140 

0.36 

0.02 

320 

6.34 

0.09 

H5 

5.89 

O.OI 

325 

4.89 

Q.l5 

H5 

0.47 

O.O2 

325 

5.87 

0.09 

I50 

5-93 

O.OI 

33° 

5.66 

o.i5 

150 

0.61 

o.o3 

33° 

5.39 

O.IO 

'55 

5-97 

O.OI 

335 

6.42 

Q.l5 

155 

0.75 

o.o3 

335 

4.87 

O.IO 

1  60 

5-99 

o.oo 

340 

7.16 

0.14 

1  60 

0.92 

o.o3 

34° 

4-35 

O.IO 

165 

5-99 

o.oo 

345 

7.87 

0.14 

165 

1.09 

p.o3 

345 

3.83 

Q.10 

170 

5.96 

O.OI 

35° 

8.54 

o.i3 

170 

1.26 

Q.04 

350 

3.33 

O.IO 

»75 

5.88 

O.02 

355 

9.14 

0.12 

175 

1.45 

0.04 

355 

2.85 

0.09 

1  80 

5-77 

o.o3 

360 

9.69 

O.II 

1  80 

1.64 

0.04 

360 

2.41 

0.08 

*s>*  The  Differences  are  calculated  for   I   Degree. 

[29] 


TABLE  V.  —  CONTINUED. 

Perturbations  of  the  Mean  Anomaly. 

Argument  18  to  25,  inclusive. 

s 

Arg. 

18. 

D. 

19. 

D. 

20. 

D. 

21. 

D. 

22. 

23.- 

24. 

25. 

0° 
IO 

20 

30 
40 

4-59 
3-96 
3-32 
2.67 
2.07 

o.63 
0.64 
o.65 
0.60 

4.82 

4-79 
4.70 

4-54 

o.o3 
0.09 

o.i  6 

0.23 

i-75 
1.48 

1.20 

o-93 
0.69 

0.27 
0.28 
0.27 
0.24 

2.21 

2.24 
2.22 
2.18 
2.10 

o.o3 

O.O2 

0.04 
0.08 

2.47 
2.46 
2.42 

2-35 
2.24 

•44 
.42 

•38 
•32 
•23 

2.08 
1.96 
1.82 
1.66 
1.48 

O.I  2 

0.05 
O.OI 
0.00 
O.OI 

5° 
60 

70 
80 
90 

1.52 

1.03 
0.62 

o.33 
0.13 

0.49 
0.41 
0.29 

O.20 

4.02 
3-69 

2.91 
2.50 

o.33 
o.38 
0.40 
0.41 

0.48 
0.30 
0.17 
0.08 
0.03 

0.18 
o.i3 
0.09 
o.o5 

1.99 

1.86 
1.70 
^•53 
^•34 

o.i3 

0.16 
0.17 
0.19 

2.09 
1.92 

1.74 

1.32 

.14 

0.92 
0.79 
0.66 

1.30 
i.  ii 
0.91- 

o-73 
0.55 

0.05 

O.II 

O.2I 
0.32 
0.45 

0.08 

0.42 

O.OI 

0.19 

IOO 

no 

1  20 
130 
140 
150 
1  60 
170 
1  80 

0.05 

O.IO 

0.25 
0.50 
0.85 
1.27 
1.78 
2.30 
2.89 

o.o5 
o.i  5 

0.25 

0.35 
0.42 
o.5i 

0.52 

o.Sg 

2.08 
1.67 
1.28 

0-93 
0.62 

o-37 
o.i  8 
0.06 
o.oo. 

0.41 
0.39 
o.35 
o.3i 

0.25 

0.19 

O.I  2 

0.06 

0.04 
0.09 

O.20 

o-34 
0-53 
0.75 

1.  00 

1.28 

i-55 

o.o5 

O.II 

0.14 
0.19 

O.22 

0.25 

0.28 
0.27 

1.15 

0.96 
0.77 
0.59 

°43 
0.29 
0.17 
0.08 
0.03 

0.19 
0.19 
0.18 
0.16 
0.14 

0.  12 

0.09 
o.o5 

i.  ii 

0.90 
0.70 
0.51 
0.36 
0.23 

O.I  2 
O.O6 
0.03 

°-53 
0.42 

0.31 

O.22 
0.13 
0.06- 
O.02 
O.OO 
O.OO 

°-39 
0.25 
0.15 
0.06 

O.O2 
O.OO 
O.O2 
0.08 

0.16 

O.6o 
0.7*5 
0.91 
.07 

•23 
•38 
•51 

•63 

•72 

o.Sg 

o.o3 

0.27 

o.o3 

190 

200 
210 
22O 

348 
4.06 

5-'7 

o.58 
0.57 
o.54 

0.03 

O.I2 

0.28 
0.51 

0.09 

o.i  6 

O.23 

1.82 

2.10 

2-37 
2.6  1 

0.28 

0.27 
0.24 

o.oo 

O.02 
O.06 
O.I4 

0.02 

0.04 
0.08 

O.O4 
0.08 
0.15 
O.26 

O.O2 
0.06 
0.12 
O.2I 

0.28 

0.42 

0.58 
0.76 

•79 

•83 
•84 
•83 

230 
240 
250 
260 
270 

5.68 
6.1  1 
6.48 
6.79 
6.99 

o.43 
0.37 
o.3i 

O.20 

0.80 

1.13 
1.51 

1.91 

2.32 

o.33 
o.38 
0.40 
0.41 

2.82 
3.00 

3.13 

3.22 

3-27 

0.18 
o.i  3 
0.09 
o.o5 

0.25 
0.38 
0.54 
0.71 
0.90 

o.i3 
0.16 
0.17 
0.19 

0.41 
0.58 
0.76 
0.97 

1.18 

0.30 
0.41 
0.52 
0.65 
0.78 

0.94 
•13 

•33 
•5i 
.69 

•79 
•73 
•63 
•52 
•39 

0.12 

0.42 

O.OI 

0.19 

280 
290 
30O 
310 
320 

33° 
34° 
350 
360 

7.11 
7.12 
7.05 
6.86 

6-55 
6.19 
5.72 
5.18 
4-59 

O.OI 

0.07 
0.19 
o.3i 
0.36 
0.47 
o.54 
0.59 

2.74 
3-15 

3-54 
3-89 
4.20 

445 
4.64 

4-75 
4.82 

0.41 
o.3g 
0.35 

o.3i 

0.25 

0.19 

O.II 

0.07 

3.26 

3.21 
3.10 

2.96 

2.77 

2-55 
2.30 

2.O2 

'•75 

o.o5 

O.II 

o.i  4 
0.19 

0.22 
0.25 
0.28 
O.27 

I.O9 
1.28 

'47 
1.65 

1.81 
1.95 

2.07 
2.16 

2.21 

0.19 
0.19 
0.18 
o.i  6 
0.14 

0.12 
0.09 

o.o5 

i.  60 
i.  80 
1.99 
2.14 
2.27 
2.38 
2.44 

2-47 

0.91 
.02 

.22 

•3' 
•38 
42 
1.44 
1.44 

.85 

•99 
2.09 
2.18 

2.22 
2.24 
2.22 
2.l6 
2.08 

.24 

.09 

o-93 
0.77 
0.61 
0.46 
o-33 

O.2I 
O.I  2 

[30] 


TABLE  V.—  CONCLUDED. 

Perturbations  of  the  Mean  Anomaly. 

Arguments  26  to  37,  inclusive. 

Arg. 

26. 

27. 

28. 

29. 

30. 

31. 

32. 

33. 

34. 

35. 

36. 

37. 

0° 

0.99 

o-34 

0.45 

0.32 

1.83 

0.91 

0.70 

0.84 

0-53 

o.oo 

0.28 

0.46 

10 

.04 

0.50 

0.36 

0.29 

2.12 

0.90 

0.68 

0.84 

0.48 

0.00 

0.31 

0.47 

20 

.05 

0.70  . 

0.28 

0.25 

2.41 

0.87 

0.65 

0.8  1 

o-43 

O.OI 

o.34 

0.48 

3° 

.06 

0.90 

O.20 

O.2I 

2.66 

0.82 

0.62 

0.77 

0.38 

O.O2 

0.36 

0.48 

40 

.06 

1.  12 

O.I3 

0.17 

2.88 

0.77 

0.59 

o-73 

0.32 

0.04 

o-37 

0.48 

5° 

.04 

i-34 

0.08 

O.I^J 

3.08 

0.71 

0-53 

0.68 

0.26 

0.07 

0-39 

0.47 

60 

.00 

1-57 

0.04 

O.IO 

3.23 

0.64 

0.47 

0.62 

O.2I 

O.IO 

0.40 

0.45 

70 

0.95 

1.78 

O.OI 

0.08 

3-32 

0.57 

0.41 

0.54 

0.16 

0.14 

0.40 

0.42 

80 

0.88 

1.98 

o.oo 

0.05 

3.38 

0.49 

0-35 

0.47 

0.12 

0.19 

o-39 

0.39 

90 

0.8  1 

2.15 

O.OI 

0.03 

3.38 

0.40 

0.29 

0.40 

0.08 

0.23 

0.38 

0.35 

IOO 

0.72 

2.30 

0.02 

O.OI 

3-34 

o-33 

0.23 

0-33 

0.04 

0.27 

0.36 

0.31 

no 

0.63 

2.42 

O.O7 

o.oo 

3-24 

0.25 

o.i  8 

0.26 

O.O2 

0.32 

°-34 

0.27 

IZO 

0.54 

2.51 

O.I  2 

o.oo 

3-.o9 

o.i  8 

0.13 

0.20 

O.OI 

0.36 

0.32 

0.23 

130 

0.44 

2.56 

o.i  8 

o.oo 

2.90 

0.13 

0.09 

0.14 

o.oo 

0.41 

0.29 

0.19 

140 

0.36 

2.56 

0.25 

O.OI 

2.68 

0.07 

0.05 

O.O9 

o.oo 

0.44 

0.25 

0.15 

150 

0.28 

2.54 

o-33 

0.03 

2.42 

0.04 

O.02 

0.05 

O.O2 

0.48 

O.22 

O.I  I 

1  60 

0.19 

2.46 

0.42 

0.05 

2.15 

O.OI 

O.OI 

O.OI 

O.05 

0.50 

O.I9 

0.08 

170 

0.12 

2.36 

0.52 

0.09 

1.86 

o.oo 

0.00 

o.oo 

0.08 

0.52 

0.15 

0.05 

1  80 

O.07 

2.22 

0.61 

O.I  2 

1-57 

O.OI 

o.oo 

o.oo 

O.I  I 

0.52 

0.12 

O.02 

190 

0.02 

2.06 

0.70 

0.15 

1.28 

0.02 

O.O2 

o.oo 

0.16 

0.52 

0.09 

O.OI 

200 

0.0  1 

1.86 

0.78 

0.19 

0.99 

0.05 

O.O5 

0.03 

O.2I 

0.51 

O.o6 

o.oo 

2IO 

o.oo 

1.66 

0.86 

0.23 

0.74 

O.IO 

0.08 

0.07 

0.26 

0.50 

0.04 

o.oo 

220 

o.oo 

1.44 

°-93 

0.27 

0.52 

0.15 

O.I  I 

O.I  I 

0.32 

0.48 

0.03 

o.oo 

230 

O.O2 

1.22 

0.98 

0.30 

0.32 

0.21 

0.17 

o.i  6 

0.38 

0.45 

O.OI 

O.OI 

240 

O.O6 

0.99 

1.02 

o-34 

0.17 

0.28 

0.23 

O.22 

°-43 

0.42 

o.oo 

0.03 

250 

O.I  I 

0.78 

1.05 

0.36 

0.08 

°-35 

0.28 

0.30 

0.48 

0.38 

o.oo 

0.06 

260 

o.i  8 

0.58 

1.  06 

0.39 

O.O2 

o-43 

o-35 

0.37 

0.52 

°-33 

O.OI 

0.09 

270 

0.25 

0.41 

1.05. 

0.41 

O.O2 

0.52 

0.41 

0.44 

0.56 

0.29 

0.02 

0.13 

280 

°-34 

O.26 

1.03 

°-43 

O.o6 

0.59 

047 

0.51 

0.60 

0.25 

0.04 

0.17 

290 

°-43 

0.14 

0.99 

0.44 

0.16 

0.67 

0.52 

0.58 

0.62 

0.2O 

0.06 

O.2I 

300 

0.52 

O.O5 

0.94 

0.44 

0.31 

0.74 

0.57 

0.64 

0.63 

0.16 

0.08 

0.25 

310 

0.62 

O.OO 

0.88 

0.44 

0.50 

0.79 

0.61 

0.70 

0.64 

O.I  I 

O.I  I 

0.29 

32O 

0.70 

o.oo 

0.8  1 

°-43 

0.72 

0.85 

0.65 

0.75 

0.64 

0.08 

0.15 

°-33 

330 

0.78 

O.O2 

0.72 

0.41 

0.98 

0.88 

0.68 

0.79 

0.62 

0.04 

0.18 

o-37 

34° 

0.87 

O.IO 

0.64 

°-39 

1.25 

0.91 

0.69 

0.83 

0.59 

0.03 

0.21 

0.40 

35° 

0.94 

0.2O 

0.54 

°-35 

1.54 

0.92 

0.70 

0.84 

0.56 

0.00 

0.25 

°-43 

360 

0.99 

0.34 

0.45 

0.32 

1.83 

0.91 

0.70 

0.84 

°-53 

o.oo 

0.28 

0.46 

[31] 


TABLE   VI. 

For  the  Terms  in  SM  to  be  Multiplied  in  t. 

Argument   10. 

0° 

I 

2 

3 

-14.521 

'4-455 
'4-383 
'4-3°7 

.066 
.072 
.076 

.081 

45° 
46 
47 
48 

-7.171 

6-934 
6.695 
6.455 

.237 
.239 
.240 
.241 

90° 

9' 
92 

93 

+   3-9°' 
4.129 

4-355 
4-579 

.228 
.226 
.224 

.222 

'35° 
136 

'37 
'38 

+  11.729 
11.835 
11.936 
12.035 

.106 

.101 

.099 

.oo5 

4 

14.226 

.087 

49 

6.214 

•  244 

94 

4.801 

.221 

'39 

12.130 

.  \j\j*j 
.092 

5 

'4-'39 

50 

5.970 

95 

5.022 

140 

12.222 

.092 

.244 

.219 

.088 

6 

-14.047 

.097 

5' 

-5.726 

.246 

96 

+   5.241 

.2l6 

141 

+  I2.3IO 

.o85 

7 

'3-95° 

.102 

S2 

5-48o 

.247 

97 

5-457 

.2l5 

142 

'2-395 

.082 

8 

13.848 

.107 

53 

5-233 

.248 

98 

5-672 

.212 

'43 

12.477 

.078 

9 

10 

'3.741 
13.630 

.III 

54 
55 

4.985 
4-736 

.249 

99 

IOO 

5.884 
6.093 

.209 

'44 
'45 

'2-555 
12.630 

/ 

.075 

.117 

.25o 

.208 

.072 

n 

—  '3-5'3 

.122 

56 

—4.486 

25o 

IOI 

+  6.301 

.  2o5 

146 

+  12.702 

12 

'3-39' 

.126 

57 

4.236 

IO2 

6.506 

.  2O2 

'47 

12.769 

'°  J[ 

'3 

13.265 

58 

3-986 

.252 

I03 

6.708 

.201 

148 

12.834 

.061 

'4 

'3-'34 

.i36 

59 

3.734 

252 

104 

6.909 

'49 

12.895 

'5 

12.998 

60 

3482 

I05 

7.107 

.19 

150 

12.952 

.007 

.141 

.252 

.I95 

.o54 

16 

'7 

-12.857 
12.712 

.145 
.i5o 

61 
62 

—  3.230 
2.977 

.253 
.253 

1  06 

107 

+   7-302 
7-495 

.193 

152 

+  13.006 
13.056 

.o5o 
f\/.t\ 

18 

12.562 

.i54 

63 

2.724 

,«•( 

108 

7.686 

,QQ 

'53 

13.101 

.U4-J 

'9 

12.408 

.i58 

64 

2.471 

.  2  J  \J 

.253 

109 

7-874 

.  X  OO 

.i85 

'54 

'3-'45 

.O4O 

20 

12.250 

65 

2.218 

IIO 

8.059 

'55 

13.185 

.i63 

.252 

.i83 

.o36 

21 

—  12.087 

.167 

66 

f 

—  1.966 

.253 

in 

+   8.242 

.179 

156 

+  13.221 

,o32 

22 

23 
24 

11.920 
11.750 
11.576 

.170 
.174 
.178 

67 
68 

69 

1.460 

1.207 

.253 
.253 
.253 

I  12 

"3 

8.421 

8.597 
8.771 

.176 
.174 
.171 

'57 
158 

'59 

13-253 
13.281 

'3-3°7 

.028 
.026 
.022 

25 

11.398 

70 

0.954 

"5 

8.942 

1  60 

'3-329 

.182 

.252 

.168 

.019 

26 

—  n.  216 

.186 

7' 

—  0.702 

.250 

116 

+  9.110 

.i65 

161 

+  13.348 

.014 

27 
28 
29 

3° 

11.030 
i  ©'.84  1 
10.648 
10.452 

.189 
.193 
.196 

72 
73 
74 
75 

•    0.452 

—  O.2OI 
+  0.049 
0.298 

.251 

.25o 

.249 

"7 
118 

"9 

120 

9.275 
9.438 
9.598 

9-755 

.i63 
.160 
'.i57 

162 
163 
164 
165 

13.362 
'3.372 
'3-38o 

'3-384 

.010 

.008 
.004 

.199 

.248 

.154 

.000 

3' 

—  10.253 

.203 

76 

+  0.546 

•  247 

121 

+  9.909 

.i5o 

1  66 

+  13-384 

,oo3 

32 
33 
34 

10.050 

9.844 
9.636 

.206 
.208 

.212 

77 
78 
79 

0-793 
1.040 
1.285 

•  *-**  / 

.247 
.245 
.245 

122 
I23 
124 

10.059 
10.206 
10.35' 

.147 
.145 
.141 

167 
168 
169 

'3-374 
'3-364 

.007 
.010 
.014 

35 

9-424 

80 

I.53O 

'25 

10.492 

170 

'3-35° 

.2l5 

.242 

.i38 

.017 

36 

37 

-  9.209 
8.992 

.217 
22O 

81 
82 

+  1.772 
2.OI4 

.242 

126 

127 

+  10.630 
10.765 

.i35 
i3a 

171 

172 

+  '3-333 
'3.3" 

.022 

38 
39 

8.772 
8.550 

.222 
.224 

83 
84 

2.255 
2-495 

.240 
.239 

128 
129 

10.897 
11.026 

»lw2 

.129 
.126 

'73 
'74 

13.286 
13.258 

.028 

.o3i 

40 

8.326 

85 

2-734 

VY 

130 

11.152 

'75 

13.227 

.226 

.236 

.122 

.035 

42 
43 
44 

—   8.100 
7.871 
7.640 
7.406 

.229 
.231 

.234 
.235 

86 

87 
88 

89 

+  2.970 
3.206 

3-439 
3.670 

.236 
.233 

.231 
.23l 

132 

'33 

'34 

+  11.274 

11.508 
11.620 

.119 
.115 
.112 
.100 

176 

'77 
178 

'79 

+  13.192 

'3-'54 
13.112 

13.067 

.o38 
.042 
.o45 
.048 

45 

7.171 

90 

3.901 

'35 

11.729 

^7 

1  80 

13.019 

[32] 


TABLE  VI.  —  CONCLUDED. 

For  the  Terms  in  &M  to  be  Multiplied  in  t. 

Argument  10.  —  Concluded. 

I 

180° 

+  13.019 

o52 

225° 

+  7.536 

.186 

270° 

-  2.442 

O/I 

315° 

—  12.050 

181 

12.967 

.o56 

226 

7.350 

.188 

271 

2.683 

.^41 

.240 

3l6 

12.207 

.i54 

182 
183 

12.91  I 

12.852 

.o5c) 
.062 

227 
228 

7.162 
6.972 

.190 
,io3 

272 
273 

2.923 
3-l63 

.240 
.24o 

317 
318 

12.361 
12.51  1 

.i5o 
.146 

184 

12.790 

.066 

229 

6.779 

.iq5 

274 

3-403 

.241 

319 

12.657 

.141 

185 

12.724 

230 

6.584 

.  «.  -y^ 

275 

3-644 

320 

12.798 

.069 

•197 

.240 

.i38 

1  86 
187 

+  12.655 

12.583 

.072 
.076 

231 
232 

+  6.387 
6.188 

.199 

.202 

276 
277 

•  3-884 
4.122 

.238 
.238 

321 

322 

—  12.936 

13.070 

'  * 

.i34 
.  i3o 

188 

12.507 

.080 

233 

5.986 

.203 

278 

4.360 

.237 

323 

13.200 

.125 

189 

12.427 

.082 

234 

5.783 

.2o5 

279 

4-597 

.237 

324 

13-325 

.120 

190 

12.345 

235 

5-578 

280 

4.834 

*  t-J  1 

325 

J3445 

.086 

.207 

.237 

.116 

191 

+  12.259 

•  OQO 

236 

+  5.371 

281 

—  5.071 

~1K 

326 

-13.561 

192 

12.169 

.OO2 

237 

5.162 

.211 

282 

5.306 

.  £.<J  J 

.235 

327    13.672 

•  108 

193 

I2.O77 

V 

.096 

238 

4-9  5  i 

.212 

283 

5-541 

.234 

328 

13.780 

.io3 

194 

I  1.981 

000 

239 

4-739 

.214 

284 

5-775 

.23l 

329 

13-883 

.098 

195 

11.882 

' 

240 

4-525 

285 

6.006 

33° 

13.981 

.102 

.2l6 

.230 

.093 

196 

+  I  1.780 

,io5 

241 

+  4.309 

286 

—  6.236 

22 

331" 

-14.074 

nfifi 

197 

11.675 

.108 

242 

4.092 

o  m 

287 

6.465 

oon 

332 

14.162 

.uoo 
nfi"? 

198 

11.567 

.112 

243 

3.873 

.219 
.221 

288 

6.694 

•"9 

.227 

333 

14.245 

•  UOO 

.070 

199 

II-455 

244 

3.652 

.223 

289 

6.921. 

.225 

334 

14.324 

/  V 
.074 

200 

11.340 

245 

3429 

290 

7.146 

335 

14.398 

.118 

.224 

.224 

.069 

2OI 

+  1  1.222 

.121 

246 

+  3.205 

.225 

291 

-  7-370 

.222 

336 

-14.467 

.o63 

202 

I  I.IOI 

.124 

247 

2.980 

.226 

292 

7.592 

.220 

337 

I4-530 

,o58 

203 
204 

10.977 
10.850 

.127 

.j3o 

248 
249 

2-754 
2-527 

.227 

293 
294 

7.812 
8.031 

.219 
on 

338 
339 

14.588 
14.642 

.o54 

205 

I0.72O 

250 

2.298 

9 

295 

8.248 

.zi  i 

34° 

14.690 

.04 

.i33 

.230 

.2l5 

.043 

206 

+  10.587 

.i35 

251 

+  2.068 

.23l 

296 

-  8.463 

.212 

341 

—  *  4-73  3 

.o38 

207 

10.452 

252 

1.837 

.23l 

297 

8.675 

.2IO 

342 

14.771 

208 

10.313 

.142 

253 

i.  606 

.233 

298 

8.885 

.208 

343 

14.803 

.026 

209 

IO.I7I 

.145 

254 

1-373 

.234 

299 

9-093 

.2o6 

344 

14.829 

.022 

2IO 

IO.O26 

255 

1.139 

300 

9.299 

345 

14.851 

.147 

.235 

.204 

.016 

21  I 

+  9.879 

.i5o 

256 

+  0.904 

.236 

301 

—  9.503 

.2OI 

346 

—  14.867 

.Oil 

212 
2I3 

9.729 
9.576 

.i53 

.156 

257 
-258 

0.668 
0.431 

.237 

237 

302 
303 

9.704 
9.902 

.198 

347 
348 

14.878 
14.884 

.006 
.001 

2I4 
215 

9420 
9.261 

.i5g 

259 
260 

+  0.194 
-0.043 

.  £*J  1 

.237 

3°4 
305 

10.097 
10.290 

.igS 

349 
350 

14.883 
14.878 

.oo5 

.162 

.238 

.199 

.012 

216 

+  9-099 

.  164 

261 

—0.281 

306 

—  10.480 

ift-T 

351 

—  14.866 

217 

218 
219 

22O 

8-935 
8.769 
8.600 
8.429 

.166 
.169 
.171 

262 
263 
264 
265 

0.520 
0.760 
.000 
.240 

.240 
.240 
.240 

307 
308 

3°9 
310 

10.667 
10.851 
1  1.032 

.11.210 

.107 
.184 
.l8l 
.178 

352 
353 
354 
355 

14.849 
14.827 
•  14.799 
14.765 

.017 

.Q22 
.028 

.o34 

.174 

.240 

.175 

.o38 

221 

222 
223 

+  8-255 
8.078 
7.900 

.177 
.178 
.181 

266 

267 
268 

£ 

-  .480 
.721 
.961 

.241 
.240 
.241 

312 

3*3 

-11.385 
11.556 
11.724 

.171 
.168 

.i65 

356 

357 
358 

-14.727 
14.684 
H-635 

.043 
•049 
.o55 

224 

7.719 

.183 

269 

2.  2O2 

.240 

3H 

11.889 

.161 

359 

14.580 

.o5o 

225 

7.536 

2"O     2.442 

3*5 

12.050 

360 

14.521 

1 

[33] 


TABLE  VII.  —  CONTINUED. 

Perturbations  of  the  Logarithm  of  the  Radius  Vector. 

Argument  1. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

V 

4!93 

32 

45° 

2263 

9r» 

90° 

2441 

3i 

135° 

3911 

23 

I 

4161 

34 

46 

2234 

•9 

28 

91 

2472 

32 

136 

3934 

23 

2 

4127 

35 

47 

2206 

27 

92 

2504 

33 

137 

3957 

22 

3 

4092 

3? 

48 

2179 

25 

93 

2537 

33 

138 

3979 

21 

4 

4°55 

38 

49 

2154 

23 

94 

2570 

33 

139 

4000 

20 

5 

4017 

5° 

2131 

95 

2603 

140 

4020 

39 

22 

34 

19 

6 

3978 

/i 

51 

2109 

96 

2637 

"U 

141 

4°39 

19 

7 

3937 

*** 
41 

52 

2089 

20 

97 

2671 

04 
34 

142 

4058 

17 

8 

3896 

42 

53 

2070 

J9 

98 

2705 

J4 

35 

H3 

4°75 

J7 

9 

3854 

44 

54 

2053 

!7 
,5 

99 

2740 

35 

144 

4092 

i5 

10 

3810 

55 

2038 

i  j 

100 

2775 

H5 

4107 

45 

i3 

36 

U 

ii 

3765 

45 

56 

2025 

12 

101 

28ll 

35 

146 

4121 

i3 

12 

3720 

/A 

57 

2013 

102 

2846 

36 

H7 

4'34 

I  2 

'3 

3674 

4U 

A~l 

58 

2003 

10 

103 

2882 

36 

148 

4146 

II 

H 

3627 

*l 

XT 

59 

1994 

9 

104 

2918 

36 

149 

4'57 

15 

358o 

*l 

60 

1987 

7 

105 

2954 

150 

4166 

48 

5 

36 

8 

16 

3532 

/a 

61 

1082 

1  06 

2990 

35 

151 

4174 

17 

3484 

40 

62 

1978' 

4 

107 

3025 

QA 

152 

4181 

6 

18 

3435 

49 

63 

1976 

2 

1  08 

3061 

ou 

35 

153 

4187 

5 

'9 

3386 

49 

64 

1976 

o 

109 

3096 

36 

^54 

4192 

3 

20 

3337 

49 

65 

1977 

I 

110 

3132 

J55 

4195 

49 

3 

36 

i 

21 

3288 

Xr\ 

66 

1980 

1  1  1 

3168 

35 

156 

4J97 

Q 

22 

3239 

49 

Kn 

67 

1984 

4 

I  12 

3203 

35 

157 

4!97 

I 

23 

3189 

•m 

/  c\ 

68 

1990 

"3 

3238 

35 

.'58 

4196 

3 

24 

3H° 

49 

/n 

69 

1997 

7 

114 

3273 

35 

159 

4!93 

25 

3091 

49 

70 

2006 

9 

115 

33°8 

1  60 

4189 

49 

10 

34 

5 

26 

3042 

/o 

7i 

2016 

116 

3342 

\ 

•!/ 

161 

4184 

27 

2994 

4o 

72 

2028 

12 

117 

3376 

O4 
»J 

162 

4J77 

7 

28 

2947 

47 

73 

2041 

i3 

118 

3410 

->4 
•3^ 

163 

4168 

9 

29 

2900 

47 

74 

2056 

i5 

119 

3444 

O  3 

32 

164 

4158 

I  O 
I  2 

30 

2853 

47 

75 

2072 

16 

1  20 

3477 

165 

4146 

31 

2807 

46 

.f 

76 

2089 

17 

121 

35io 

33 

32 

1  66 

4J32 

14 

,4E 

32 

2761 

46 

77 

2108 

'9 

122 

3542 

32 

167 

4117 

1  J 

33 

2717 

44 

78 

2127 

19 

I23 

3574 

3i 

168 

4100 

n 

34 

2673 

44 

.  T 

79 

2148 

21 

124 

3605 

3i 

169 

4081 

'9 

35 

2630 

4J 

80 

2170 

22 

125 

3636 

170 

4061 

2Q 

36 

2588 

42 

81 

2193 

23 

126 

3666 

3o 

Ir. 

171 

0941 

22 
o  / 

37 

2547 

4i 

82 

2217 

24 

127 

3696 

oO 

172 

4015 

^4 
nA 

38 

2507 

4o 

83 

2242 

25 

128 

3725 

29 
oft 

173 

3989 

xu 

39 

2469 

38 

84 

2268 

26 

I29 

3753 

2o 
•fl 

174 

3962 

27 

9r» 

40 

2431 

38 

85 

2295 

27 

I30 

378i 

2o 

'75 

3933 

29 

41 

2395 

36 

86 

2323 

28 

I31 

3808 

27 

1  76 

39°3 

3o 

32 

42 

2360 

35 

87 

235* 

28 

132 

3835 

27 

177 

3871 

•)/ 

43 

2326 

34 

88 

2380 

29 

J33 

3861 

26 

c 

178 

3837 

04 

9A 

44 

2294 

32 

89 

2410 

3o 

134 

3886 

25 

179 

3801 

ou 

•3- 

45 

2263 

3i 

90 

2441 

3i 

135 

3911 

25 

1  80 

3764 

J7 

[34] 


TABLE  VII.  —  CONTINUED. 

Perturbations  of  the  Logarithm  of  the  Radius  Vector. 

Argument  1  .  —  Concluded. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 
t.  * 

Eq. 

D. 

Arg. 

Eq. 

D. 

1  80° 

3764 

225° 

990 

61 

270° 

356 

44 

315° 

345  * 

63 

181 

3725 

X  I 

226 

929 

60 

271 

400 

46 

316 

35*4 

62 

182 

3684 

41 

227 

869 

272 

446 

i\\j 

48 

3^7 

3576 

183 

3641 

44 

228 

810 

57 

273 

494 

5o 

3l8 

3636 

58 

184 

3597 

46 

229 

753 

56 

274 

544 

53 

319 

3694 

57 

185 

355i 

230 

697 

275 

597 

320 

3751 

47 

54 

55 

54 

1  86 

3504 

An 

231 

,643 

52 

276 

652 

56 

321 

3805 

53 

187 

3455 

49 

5i 

232 

591 

5o 

277 

708 

5o 

322 

3858 

5o 

188 

34°4 

52 

233 

541 

49 

278 

767 

jy 
60 

323 

3908 

JW 

40 

189 

335.2 

53 

234 

492 

46 

279 

827 

62 

324 

3957 

**•/ 

/A 

190 

3299 

235 

446 

l\\J 

280 

889 

325 

4003 

4U 

55 

45 

64 

44 

191 

3244 

236 

401 

281 

953 

65 

326 

4047 

192 

3188 

K.Q 

237 

359 

/  1 

282 

1018 

At 

327 

4090 

* 

193 

3130 

Do 

c 

238 

3^8 

41 
38 

283 

1085 

07 
AQ 

328 

4130 

4o 

194 

3071 

59 
60 

239 

280 

36 

284 

"53 

uo 

7° 

329 

4167 

36 

«95 

3011 

240 

244 

285 

1223 

33° 

4203 

61 

34 

71 

33 

196 

2950 

241 

210 

286 

1294 

331 

4236 

197 

2887 

63 

242 

179 

3i 

287 

1366 

72 

332 

4267 

3i 

198 

2824 

63 
65 

243 

150 

29 
26 

288 

H39 

73 

333 

4295 

28 
26 

199 

2759 

244 

I24 

289 

1512 

/ 

334 

43  2I 

200 

2694 

65 

245 

IOO 

24 

290 

1587 

75 

335 

4345 

24 

201 

26*8 

66 

246 

78 

22 

291 

1663 

76 

»A 

336 

4366 

21 

2O2 

2561 

67 

247 

59 

J9 

rA 

292 

1739 

76 

337 

4385 

19 

203 

2494 

67 

248 

43 

IO 

293 

1816 

77 

338 

4402 

17 

204 

2426 

68 
f 

249 

29 

14 

294 

1893 

77 

_Q 

339 

4416 

14 

205 

2357 

69 

250 

18 

I  I 

295 

1971 

7° 

34° 

4428 

12 

2O6 

2288 

69 

251 

10 

8 

296 

2049 

78 

_o 

H, 

4437 

9 

207 

2218 

79 

252 

4 

O 

297 

2127 

78 

342 

4444 

1 

208 

2148 

70 

253 

i 

O 

298 

2205 

_Q 

343 

4448 

4 

209 

2078 

70 

254 

i 

0 

299 

2283 

78 

344 

4450 

2 

210 

2007 

71 

255 

3 

2 

300 

2361 

7 

345 

4450 

0 

21  I 

1936 

7i 

256 

8 

5 

Q 

301 

2439 

78 

346 

4448 

2 

212 

1866 

70 

257 

16 

O 

302 

2516 

77 

347 

4443 

2I3 

1796 

70 

258 

26 

10 

3°3 

2593 

77 

348 

443  6 

7 

2I4 

1725 

71 

259 

39 

1 

304 

2670 

77 

.A 

349 

4427 

9 

2I5 

1655 

70 

260 

55 

1 

3°5 

2746 

7° 

350 

4416 

1  1 

70 

19 

75 

14 

216 

1585 

6n 

261 

74 

306 

2821 

351 

440.2 

217 

1516 

09 

68 

262 

95 

2  1 

307 

2896 

7 

352 

4387 

i5 

218 

1448 

68 

263 

119 

26 

308 

2969 

73 

353 

4370 

J7 

219 

1380 

68 

264 

1  45 

3°9 

3042 

T  1 

354 

435° 

20 

220 

1312 

265 

29 

310 

71 

355 

4328 

22 

66 

32 

70 

23 

221 

1246 

66 

266 

206 

311 

3183 

356 

43°5 

26 

222 

1  1  80 

267 

240 

1A 

312 

3252 

AQ 

357 

4279 

223 

1116 

Ax 

268 

276 

Ou 

313 

3320 

uo 

66 

358 

4252 

27 

224 

1052 

U4 
62 

269 

315 

A\ 

3H 

3386 

65 

359 

4224 

3, 

225 

99° 

270 

356 

4* 

3i5 

345' 

360 

4193 

[35] 


TABLE  VII.—  CONTINUED. 

Perturbations  of  the  Logarithm  of  the  Radius  Vector. 

Argument  2. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

0° 

3644 

23 

45° 

1940 

/Q 

9°° 

178 

2O 

135° 

3" 

i 

3621 

24 

46 

1892 

40 

48 

91 

158 

18 

136 

33° 

20 

^ 

3597 

47 

1844 

Xn 

92 

140 

18 

'37 

35° 

i  n 

3 

3573 

26 

48 

'795 

49 

48 

93 

122 

16 

138 

369 

•V 

2O 

4 

3547 

26 

49 

1747 

48 

94 

1  06 

i5 

139 

389 

20 

5 

3521 

50 

1699 

95 

91 

140 

409 

27 

48 

14 

20 

6 

3494 

9-7 

5' 

1651 

96 

77 

i3 

141 

429 

7 

3467 

J  / 

52 

1603 

48 

97 

64 

142 

449 

2O 
2O 

8 

3438 

29 

53 

1555 

48 

98 

53 

ii 

H3 

469 

20 

9 

34°9 

3o 

54 

1507 

47 

99 

42 

144 

489 

2O" 

10 

3379 

55 

1460 

IOO 

33 

H5 

509 

3i 

47 

8 

20 

1  1 

3348 

56 

1413 

XT 

101 

25 

146 

529 

12 

•3, 

57 

1366 

4-7 

102 

18 

7 

H7 

549 

2O 

13 

3284 

O  ^ 

33 

58 

»3'9 

46 

103 

12 

4 

148 

568 

2O 

H 

3Z51 

V 

59 

1273 

104 

8 

149 

588 

15 

3217 

60 

1227 

4 

105 

4 

150 

607 

'9 

34 

46 

2 

10 

16 

3183 

61 

1181 

1  06 

2 

I  r  i 

626 

7 

i? 

3H8 

3D 

62 

1  136 

XX 

I07 

O 

2 

152 

645 

19 

18 

3112 

63 

1092 

44 
XX 

108 

0 

O 

153 

664 

19 

'9 

3°75 

37 

64 

1048 

44 

44 

109 

I 

2 

154 

683 

J9 
18 

20 

3038 

7 

65 

1004 

IIO 

3 

155 

701 

38 

43 

3 

_ 

18 

21 

3000 

In 

66 

961 

xl 

in 

6 

I56 

•719 

ifi 

22 

2961 

J9 

67 

918 

40 

I  12 

10 

4 

157 

737 

1  O 

23 

2922 

Xn 

68 

877 

XI 

113 

15 

K 

I58 

754 

17 

24 

2882 

40 
/  n 

69 

836 

m 
/.  i 

114 

20 

3 

159 

771 

' 

2842 

4O 

70 

795 

4^ 

27 

7 

1  60 

787 

1 

41 

4o 

8 

16 

26 

2801 

/  w 

71 

755 

116 

35 

161 

803 

16 

27 

2760 

41 

72 

717 

9Q 

117 

43 

162 

819 

i5 

28 

2718 

43 

73 

679 

OO 

38 

118 

53 

10 

163 

834 

i5 

29 

2675 

x3 

74 

641 

119 

63 

10 

164 

849 

T  X 

3° 

2632 

40 

75 

605 

1  20 

74 

1  1 

165 

863 

14 

44 

35 

12 

14 

31 

2588 

44 

76 

570 

35 

121 

86 

12 

1  66 

/- 

877 

i3 

32 

2544 

44 

77 

535 

34 

122 

9.8 

l3 

167 

890 

i3 

33 

2500 

A5 

78 

501 

7o 

I23 

in 

168 

9°3 

I  2 

34 

2455 

(t*j 

45 

79 

469 

O  £ 

32 

124 

125 

i5 

169 

915 

12 

35 

2410 

80 

437 

I25 

140. 

170 

927 

46 

3i 

i5 

11 

36 

2364 

81 

406 

126 

155 

.K 

171 

938 

1  1 

37 

2318 

/{. 

82 

376 

° 

I27 

170 

J  J 

172 

949 

38 

2272 

40 

47 

83 

347 

29 

2T 

128 

1  8.6 

17 

173 

960 

10 

39 

2225 

'  /.n 

84 

320 

'  / 

129 

203 

174 

970 

I  O 

40 

2178 

47 

85 

293 

27 

130 

220 

'7 

17S 

980 

41 

2131 

47 

/Q 

86 

268 

25 

I31 

237 

17 
iR 

176 

989 

9 

42 

2083 

4o 

87 

243 

no 

I32 

255 

1  o 

,Q 

177 

998 

9 

43 

2036 

47 

88 

220 

2o 

133 

273 

1  O 

178 

1006 

44 

1988 

4 

89 

199 

21 

134 

292 

J9 

i  n 

179 

1014 

i 

45 

1940 

90 

178 

2  1 

'35 

311 

'9 

1  80 

1021 

i 

[36] 


TABLE  VII.—  CONTINUED. 

Perturbations  of  the  Logarithm  of  the  Radius  Vector. 

Argument  2.  —  Concluded^ 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg.     Eq. 

D. 

Arg. 

Eq. 

D. 

1  80° 

1021 

225° 

1184 

270° 

2275 

_ 

315° 

3744 

18 

181 

1028 

1 
6 

226 

1103 

9 

271 

2312 

38 

316 

3762 

18 

182 

1034 

A 

227 

I  2O2 

9 

272 

2350 

38 

3*7 

3780 

16 

183 

1040 

U 
K. 

228 

1213 

1  1 

273 

2388 

38 

318 

3796 

184 

1045 

J 

5  . 

229 

1224 

11 

274 

2426 

38 

319 

3811 

i5 

185 

1050 

230 

IZ35 

275 

2464 

320 

3826 

5 

12 

38 

14 

186 

1055 

231 

1247 

276 

2502 

3o 

321 

3840 

i3 

187    1059 

232 

1260 

1 

277 

2541 

V 

38 

322 

3853 

188 

1063 

/ 

233 

1274 

14 

278 

2579 

323 

3865 

1  2 

189 

1067 

4 

3 

234 

1288 

i4 
i5 

279 

2618 

38 

324 

3876 

1  1 

190 

1070 

235 

'3°3 

280 

2656 

325 

3886 

1  0 

3 

16 

38 

9 

191 

1073 

3 

236 

1319 

-  A 

281 

2694 

38 

326 

3895 

192 

1076 

2 

237 

1335 

10 

282 

2732 

38 

327 

39°3 

193 

1078 

•} 

238 

1352 

D 

283 

2770 

38 

328 

3910 

7 

194 

1081 

o 

239 

1370 

IO 

284 

2808 

38 

329 

3916 

6 

1083 

240 

1389 

19 

285 

2846 

330 

3921 

5 

2 

20 

38 

4 

196 

1085 

2 

241 

1409 

286 

2884 

331 

3925 

197 

1087 

242 

1429 

20 

287 

2921 

7 

332 

3928 

3 

198 

1089 

2 

243 

1450 

21 

288 

2958 

7 

333 

393° 

2 

199 

1091 

I 

244 

1472 

22 
23 

289 

2995 

36 

334 

3932 

2 

200 

1092 

245 

1495 

290 

3031 

335 

3932 

o 

2 

23 

36 

2OI 

1094 

I 

246 

1518 

24 

291 

3067 

36 

336 

3931 

I 

2O2 

1095 

247 

1542 

292 

3^3 

337 

3930 

i 

203 

1097 

248 

1567 

25 

293 

3138 

i/ 

338 

3928 

2 

204 

1098 

249 

1593 

nA 

294 

3172  • 

04 

o/ 

339 

3924 

4 

2O5 

I  1  00 

2 

250 

1619 

20 

295 

3206 

04 

34° 

3920 

4 

206 

IIOI 

i 

251 

1646 

27 

no 

296 

3239 

33 

QT 

341  ' 

39'5 

5 

207 

1103 

2 

252 

1674 

2o 

297 

3272 

vd 

342 

39°9 

6 

208 

1105 

2 

253 

1703 

29 

298 

33°4 

32 

343 

3902 

7 

2O9 

1107 

2 

254 

1732 

29 

299 

3336 

3i 

344 

3894 

210 

1  109 

2 

255 

1762 

° 

300 

3367 

345 

3885 

9 

2 

3o 

3o 

10 

211 

II  II 

•J 

256 

1792 

fo 

301 

3397 

3o 

346 

3875 

i  j 

212 

1114 

•j 

0 

257 

1824 

O  £ 

302 

3427 

347 

3864 

I  T 

2I3 

1117 

o 

0 

258 

1855 

1 

3°3 

3456 

28 

348 

3852 

I  £. 

I  2 

2I4 

I  120 

ij 

259 

1887 

2 

3°4 

3484 

28 

349 

3840 

215 

I  124 

4 

260 

1920 

3°5 

3512 

35° 

3826 

14 

4 

33 

27 

14 

216 

1128 

261 

'953 

306 

3539 

351 

3812 

217 

II32 

4 

262 

1987 

34 
35 

3°7 

3566 

27 

25 

352 

3796 

1 

218 

I  137 

263 

2O22 

TS 

308 

3591 

353 

378o 

1 

219 

1142 

. 

264 

2057 

O  J 

3°9 

3615 

24 

2 

354 

3764 

«8 

22O 

1148 

265 

2092 

3 

310 

3639 

355 

3746 

lu 

6 

36 

23 

ID 

221 

1154 

266 

2128 

311 

3662 

22 

356 

3727 

*  V 

222 

1  161 

7 

267 

2164 

312 

3684 

2  I 

357 

3708 

19 

223 

1168 

7 
8 

268 

22OI 

37 

313 

3705 

2O 

358 

3688 

2O 

224 

1  176 

8 

269 

2238 

7 

3H 

3725 

359 

3666 

22 

225      1184 

270    2275 

3^5 

3744 

. 

360 

3644 

22 

[37] 


TABLE  VII.  —  CONTINUED. 

Perturbations  of  the  Logarithm  of  the  Radius  Vector. 

Argument  3. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

0° 

1484 

47 

45° 

8l 

I  2 

9°° 

481 

135° 

2433 

53 

I 

H37 

*  / 

46 

46 

69 

II 

91 

5IO 

3i 

I36 

2486 

54 

2 

'39* 

45 

47 

58 

92 

frH 

3i 

137 

2540 

53 

3 

1346 

45 

48 

48 

93 

572 

3i 

138 

2593 

54 

4 

1301 

44 

49 

39 

9 
o 

94 

603 

33 

2647 

•JiJ. 

54 

5 

1257 

5° 

30 

7 

95 

636 

140 

2701 

44 

"J 

34 

54 

6 

1213 

43 

51 

23 

6 

96 

670 

34 

141 

2755 

54 

7 

1170 

43 

S2 

17 

5 

97 

704 

35 

142 

2809 

8 

1127 

^M 

42 

53 

12 

5 

98 

739 

36 

143 

2863 

54 

9 

1085 

4i 

54 

7 

3 

99 

775 

36 

144 

2917 

54 

10 

1044 

55 

4 

IOO 

8n 

145 

2971 

4t 

21 

37 

54 

n 

1003 

56 

2 

2 

101 

848 

38 

146 

3025 

54 

12 

964 

40 

57 

0 

O 

102 

886 

3o 

H7 

3°79 

<JQ 

55 

13 

924 

38 

58 

0 

Q 

I03 

925 

7 

148 

3J34 

54 

14 

886 

38 

59 

O 

2 

104 

964 

3q 

1  49 

3188 

54 

'5 

848 

60 

2 

105 

1003 

•jy 

150 

3242 

37 

2 

4o 

54 

16 

8n 

61 

4 

1  06 

I043 

151 

3296 

17 

774 

37 

62 

8 

I07 

1085 

42 

152 

335° 

lit 

18 

739 

VI 

62 

12 

6 

108 

1126 

4i 

153 

34°4 

J4 

'9 

704 

35 

64 

18 

6 

109 

1168 

43 

3458 

54 

20 

669 

65 

24 

no 

121  I 

155 

3512 

34 

7 

43 

54 

21 

635 

66 

31 

in 

1254 

/K. 

156 

3566 

22 

603 

2 

67 

40 

9 

112 

I299 

4J 

157 

3620 

f.-i 

23 

571 

2 
2 

68 

49 

9 
10 

"3 

1343 

45 

158 

3673 

j\} 

54 

24 

539 

69 

59 

1  1 

114 

I388 

/A 

159 

3727 

*^4 

53 

25 

509 

° 

70 

70 

"5 

H34 

40 

1  60 

3780 

3o 

12 

46 

•53 

26 

479 

oft 

71 

82 

i3 

116 

1480 

161 

3833 

53 

27 

451 

vo 

oft 

72 

95 

117 

1527 

/-. 

162 

3886 

52 

28 

423 

20 

28 

73 

109 

118 

1574 

47 

163 

3938 

52 

29 

395 

74 

123 

16 

119 

1621 

48 

164 

399° 

52 

30 

369 

3 

75 

139 

1  20 

1669 

,65 

4042 

25 

17 

48 

52 

31 

344 

mK 

76 

156 

121 

1717 

Xn 

1  66 

4094 

5i 

32 

3^9 

J  J 

77 

173 

J7 
18 

122 

1766 

49 

Xn 

167 

4H5 

5i 

33 

296 

2 

78 

191 

20 

I23 

1815 

49 

1  68 

4196 

5i 

34 

273 

32 

79 

211 

20 

124 

1865 

5o 

169 

4247 

5o 

35 

251 

80 

231 

I25 

1915 

170 

4297 

21 

21 

5i 

5o 

36 

230 

21 

81 

252 

22 

126 

1966 

5i 

171 

4347 

5o 

37 

209 

82 

274 

23 

127 

2017 

5i 

172 

4397 

40 

38 

190 

18 

83 

297 

23 

128 

2068 

5i 

173 

4446 

*+•/ 
49 

39 

172 

18 

84 

320 

25 

I29 

21  19 

52 

174 

4495 

48 

40 

154 

85 

345 

130 

2I7I 

175 

4543 

16 

26 

53 

48 

41 

138 

16 

86 

371 

131 

2224 

53 

176 

4591 

42 

122 

i5 

87 

397 

28 

132 

2277 

52 

177 

4638 

47 

43 

I07 

88 

424 

28 

133 

2329 

52      . 

178 

4685 

4/ 

47 

44 

94 

i3 

89 

452 

134 

2381 

52 

179 

4732 

46 

45 

81 

90 

481 

135 

2433 

1  80 

4778 

[38] 


TABLE  VII.  —  CONTINUED. 

Perturbations  of  the  Logarithm  of  the  Radius  Vector. 

Argument  3.  —  Concluded.- 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

180° 

4778 

xfi 

225° 

6159 

12 

270° 

5783 

2O 

315° 

3852 

53 

181 

4824 

4U 
/5 

226 

6171 

|| 

271 

5754 

zy 
2O 

316 

3799 

53 

182 

4869 

i|.J 
// 

227 

6182 

IO 

272 

5725 

"V 
3l 

317 

3746 

54 

183 

49'  3 

44 
AA 

228 

6192 

10 

273 

5694 

3l 

3i8 

3692 

*w^ 

53 

184 

4957 

44 
AA 

229 

6202 

8 

274 

5663 

32 

319 

3639 

54 

185 

5001 

4^4- 

230 

62IO 

275 

5631 

320 

3585 

43 

7 

33 

54 

1  86 

5044 

/  n 

231 

6217 

276 

5598 

•\/. 

321 

353i 

«x 

187 

5086 

4J 

/9 

232 

6224 

7 
5 

277 

5564 

04 
34 

322 

3477 

J4 

55 

1  88 

5128 

4^ 

/,  T 

233 

6229 

278 

5530 

3A 

323 

3422 

5A 

189 

5169 

41 
A  T 

234 

6233 

x 

279 

5496 

*-*4 

36 

324 

3368 

J4 

55 

190 

5210 

41 

235 

6237 

4 

280 

5460 

325 

3313 

4o 

3 

36 

55 

191 

5250 

In 

236 

6240 

281 

5424 

•)- 

326 

3258 

Kf. 

192 

5289 

6() 
Irv 

237 

6241 

I 

282 

5387 

J7 

•3Q 

327 

3203 

•JJ 
KR 

193 

5328 

J9 

T8 

238 

6242 

I 

283 

5349 

•JO 

38 

328 

3H8 

•JJ 
*>/. 

194 

5366 

OO 

o.-i 

.    239 

6242 

0 

284 

53" 

3r> 

329 

3°94 

J4 

K, 

195 

5403 

J7 

240 

6241 

I 

285 

5272 

*9 

33° 

3040 

J4 

87 

2 

4o 

54 

196 

5440 

or 

241 

6239 

286 

5232 

331 

2986 

re 

197 

5475 

65 

242 

6236 

. 

287 

5192 

40 

332 

2931 

D3 

K.K. 

198 

55" 

36 

0  K 

243 

6232 

4 

288 

5'5' 

4i 

333 

2876 

55 

e  / 

199 

5546 

o5 

0.  O. 

244 

6228 

4 

289 

5109 

42 

/O 

334 

2822 

54 

ec 

200 

5579 

OO 

245 

6222 

290 

5067 

42 

335 

2767 

DO 

2OI 

5612 

33 

ort 

246 

6215 

7 

291 

5024 

43 

/O, 

336 

2713 

54 

r  / 

2O2 

5644 

O2 
"Jo 

247 

6208 

7 

292 

4981 

4-J 
/  / 

337 

2659 

04 
c  / 

203 

5676 

O  2 
•3n 

248 

6  1  99 

9 

293 

4937 

44 
/* 

338 

2605 

a4 

c  / 

204 

5706 

ou 

7n 

249 

6189 

10 

294 

4892 

4J 
/K. 

339 

2551 

04 

r  / 

205 

5736 

OO 

250 

6179 

IO 

295 

4847 

4J 

340 

2497 

54 

29 

11 

46 

53 

2O6 

5765 

On 

251 

6168 

,0 

296 

4801 

X6 

34i 

2444 

CO 

207 

5794 

29 

252 

6155 

IO 

,0 

297 

4755 

4U 
/A 

342 

2391 

Do 

c  . 

208 

5821 

27 

253 

6142 

IO 

298 

4709 

40 
XT 

343 

2337 

54 

CO 

209 

5848 

27 
26 

254 

6128 

14 
i^ 

299 

4662 

47 
/8 

344 

2284 

JO 
fio 

210 

5874 

255 

6113 

ID 

300 

4614 

40 

345 

2232 

J2 

25 

16 

48 

52 

21  I 

5899 

OX 

256 

6097 

,A 

301 

4566 

Xr» 

346 

2180 

52 

212 

5923 

~4 

o  / 

257 

6081 

1  U 

T  Q 

302 

45'7 

49 

347 

2128 

£<1 

213 

5947 

•^4 
2  2 

258 

6063 

10 

3°3 

4468 

49 

/r\ 

348 

2076 

02 

^T 

214 

5969 

259 

6044 

!9 

3°4 

4419 

49 

*ir> 

349 

2024 

33 

£.» 

215 

5991 

22 

260 

6025 

*9 

3°5 

4369 

JO 

35° 

'973 

01 

21 

21 

5o 

5i 

216 

6012 

261 

6004 

306 

4319 

'in 

35i 

1922 

*;r> 

2I7 

6032 

20 

262 

5983 

21 

3°7 

4269 

JU 

/;, 

352 

1872 

JO 

f\n 

218 

6051 

:9 

,Q 

263 

5961 

22 

nl 

308 

4218 

>ji 

R, 

353 

1822 

oo 

Ar^ 

219 

6069 

1  O 

264 

5938 

2J 

3°9 

4167 

VI 
C9 

354 

1772 

DO 

220 

6086 

J7 

265 

5914 

24 

310 

4115 

J  6 

355 

1723 

4t> 

16 

25 

52 

4o 

221 

6102 

TA 

266 

5889 

n^ 

311 

4063 

«9 

356 

1674 

^y 

yO 

222 

6118 

1  U 

tS 

267 

5864 

2  J 

312 

4011 

v« 

53 

357 

1626 

4» 

/Q 

223 

6i33 

1  J 

it, 

268 

5837 

27 

3*3 

3958 

*;•) 

358 

1578 

40 

224             6146 

rvj 
,-3 

269 

5810 

27 

01 

3«4l 

39°5 

JO 
S-3 

359 

J53i 

47 

225             6159 

1 

1  0 

270 

5783 

27 

3i5 

3852 

>JO 

360 

1484 

47 

[39] 


TABLE  VII.  —  CONTINUED. 

Perturbations  of  the  Logarithm  of  the  Radius  Vector. 

Argument  4. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

0° 

340 

I  O 

45° 

5OI 

6 

90° 

77 

135° 

"5 

Q 

i 

35° 

IO 

46 

495 

6 

91 

70 

7 

136 

123 

O 

Q 

2 

360 

47 

489 

92 

63 

7 

137 

131 

O 
Q 

3 

369 

10 

48 

482 

7 

93 

56 

7 
1 

138 

139 

O 

8 

4 

379 

49 

475 

94 

49 

i 

139 

H7 

0 

5 

388 

9 

5° 

468 

95 

43 

140 

155 

o 

9 

8 

6 

8 

6 

397 

51 

460 

Q 

96 

37 

141 

163 

7 

406 

9 

52 

452 

O 

8 

97 

32 

A 

142 

172 

9 

8 

4«5 

9 

53 

444 

Q 

98 

27 

J 

£j 

H3 

1  80 

9 

424 

9 

54 

43  6 

O 

99 

22 

J 

144 

189 

9 

10 

433 

9 

55 

427 

9 

IOO 

18 

197 

. 

8 

9 

4 

8 

1  1 

441 

8 

56 

418 

101 

14 

3 

146 

205 

8 

12 

449 

57 

409 

102 

1  1 

H7 

213 

13 

457 

58 

399 

IO 

103 

8 

148 

221 

8 

H 

465 

59 

389 

10 

104 

6 

2 

148 

229 

15 

472 

7 

60 

379 

I  O 

105 

4 

2 

150 

237 

16 

479 

7 

61 

369 

IO 

1  06 

2 

2 

'51 

245 

8 

17 

485 

6 

62 

359 

IO 

I07 

I 

I 

152 

252 

1 

18 

491 

6 

63 

348 

1  1 

108 

O 

I 

260 

8 

'9 

497 

6 

64 

338 

10 

109 

0 

0 

154 

267 

7 

20 

503 

6 

65 

327 

1  1 

I  10 

o 

O 

'55 

274 

7 

21 

508 

5 

66 

316 

II 

in 

o 

0 

156 

28l 

7 

22 

5*3 

5 

67 

305 

1  1 

112 

I 

I 

157 

288 

7 

23 

4 

68 

294 

1  1 

113 

2 

I 

158 

294 

6 

24 

521 

4 

69 

283 

I  I 

114 

4 

2 

300 

6 

25 

525 

4 

70 

272 

I  I 

"5 

6 

2 

1  60 

306 

6 

26 

528 

3 

71 

261 

II 

116 

8 

2 

161 

312 

6 

27 

3 

72 

250 

1  1 

117 

1  1 

Q 

162 

317 

5 

28 

534 

73 

240 

IO 

118 

»4 

•3 

163 

322 

5 

29 

535 

I 

74 

229 

I  I 

119 

18 

4 

164 

327 

5 

30 

536 

i 

75 

218 

I  I 

1  20 

22 

4 

165 

331 

4 

3' 

537 

I 

76 

207 

II 

121 

26 

4 

A. 

1  66 

335 

4 

32 

537 

o 

77 

197 

122 

31 

J 

167 

339 

4 

33 

537 

o 

78 

1  86 

1  I 

123 

36 

e 

168 

342 

34 

537 

o 

79 

176 

124 

41 

D 

169 

345 

35 

536 

I 

80 

1  66 

10 

I25 

46 

170 

348 

2 

10 

6 

3 

36 

534 

81 

156 

126 

52 

171 

35' 

37 

532 

2 

82 

146 

1  0 

I27 

58 

172 

353 

2 

38 

53° 

2 

0 

83 

136 

IO 

128 

64 

173 

355 

2 

39 

527 

j 

84 

127 

9 

I29 

70 

'74 

357 

2 

40 

524 

85 

118 

9 

130 

77 

7 

i75 

358 

I 

4, 

520 

4 

86 

109 

9 

131 

84 

7 

D 

176 

359 

I 

42 

516 

87 

101 

Q 

132 

92 

O 

177 

359 

O 

43 

51  1 

88 

93 

O 

133 

99 

7 

Q 

178 

359 

C 

44 

506 

5 

89 

85 

8 

X34 

107 

O 

8 

179 

359 

O 

45 

501 

90 

77 

'35 

"5 

1  80 

358 

[40] 


TABLE  VII.—  CONTINUED. 

Perturbations  of  the  Logarithm  of  the  Radius  Vector. 

Argument  4.  —  Concluded-. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

1  80° 

358 

225° 

209 

270° 

245 

Q 

315° 

114 

2 

181 

357 

i 

226 

207 

2 

271 

245 

| 

316 

112 

2 

182 

356 

i 

227 

206 

I 

272 

244 

o 

317 

I  IO 

I 

183 

355 

i 

228 

205 

I 

273 

244 

I 

3i8 

IO9 

I 

184 

354 

i 

229 

204 

I 

274 

243 

J 

3J9 

108 

j 

185 

352 

2 

230 

203 

I 

275 

242 

320 

107 

2 

I 

I 

O 

1  86 

35° 

Q 

231 

2O2 

o 

276 

241 

2 

321 

107 

O 

187 

347 

ij 

232 

202 

277 

239 

322 

107 

188 

344 

3 

233 

2O2 

0 

278 

238 

I 

2 

323 

107 

O 

189 

341 

3 

234 

2O2 

O 

279 

236 

2 

324 

108 

1 

190 

338 

235 

2O2 

o 

280 

234 

325 

109 

3 

0 

2 

I 

191 

335 

236 

2O2 

I 

281 

232 

3 

326 

no 

2 

192 

33i 

4 

237 

203 

I 

282 

229 

2 

327 

112 

2 

193 

328 

3 

238 

204 

J 

283 

227 

3 

328 

II4 

2 

194 

3H 

4 

239 

205 

J 

284 

224 

3 

329 

116 

3 

195 

320 

4 

240 

2O6 

285 

221 

33° 

119 

I 

3 

3 

196 

316 

241 

207 

2 

286 

21  8 

3 

33i 

122 

3 

197 

312 

242 

209 

287 

215 

332 

125 

198 

308 

4 
^ 

243 

2IO 

2 

288 

211 

3 

333 

129 

4 

199 

3°3 

3 

244 

212 

I 

289 

208 

4 

334 

133 

5 

200 

299 

245 

213 

290 

204 

335 

138 

5 

2 

4 

5 

2OI 

•  294 

246 

215 

j 

291 

2OO 

336 

'43 

2O2 

290 

4 

K 

247 

216 

2 

292 

196 

x 

337 

148 

203 

285. 

J 

248 

218 

I 

293 

I92 

4 

338 

»54 

204 

281 

4 

249 

219 

2 

294 

188 

339 

I  60 

205 

276 

250 

221 

295 

184 

4 

34° 

1  66 

206 

272 

4 

251 

223 

2 
2 

296 

1  80 

4 

34i 

173 

7 

207 

268 

4 

252 

225 

1 

297 

176 

342 

1  80 

1 

208 

263 

253 

226 

2 

298 

172 

4 

343 

187 

1 

209 

259 

4 

254 

228 

2 

299 

168 

344 

194 

1 

210 

255 

4 

255 

230 

300 

164 

345 

202 

211 

251 

4 

256 

232 

2 

301 

1  60 

4 

346 

210 

8 

212 

247 

4 

257 

234 

2 

302 

156 

4 

347 

219 

9 

213 

243 

4 

258 

235 

I 

3°3 

152 

4 

348 

227 

214 

239 

4 

259 

237 

2 

3°4 

148 

4  . 

349 

236 

9 

2I5 

235 

4 

260 

238 

I 

305 

144 

4 

35° 

245 

9 

216 

232 

3 

Q 

261 

239 

I 

306 

140 

4 

351 

254 

9 

2I7 

229 

<J 
3 

262 

240 

I 

3°7 

136 

4 

352 

263 

9 

218 

226 

O 

3 

263 

241 

I 

308 

133 

353 

272 

9 

219 

223 

T 

264 

242 

I 

3°9 

130 

354 

28l 

9 

22O 

220 

tf 

265 

243 

I 

310 

127 

355 

291 

IO 

221 

217 

3 

266 

244 

I 

311 

124 

3 

356 

301 

10 

222 

2I5 

2 

267 

244 

O 

312 

121 

3 

357 

3IO 

9 

223 

213 

2 

268 

245 

I 

313 

II9 

2 

358 

320 

IO 

224 

21  I 

2 
2 

269 

245 

O 

3H 

116 

3 

359 

33° 

10 

225 

209 

270 

245 

0 

3i5 

114 

2 

360 

34° 

10 

[41] 


TABLE  VII.—  CONTINUED. 

Perturbations  of  the  Logarithm  of  the  Radius  Vector. 

Argument  5. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

0° 

929 

45° 

I65 

1  0 

90° 

32 

5 

135° 

538 

i 

907 

22 

46 

155 

IO 

91 

37 

5 

136 

555 

18 

2 

885 

2  1 

47 

'45 

10 

92 

42 

5 

'37 

573 

1  1 

3 

864 

22 

48 

135 

IO 

93 

47 

A 

138 

59° 

1  1 
18 

4 

842 

49 

125 

94 

53 

U 

139 

608 

18 

5 

821 

2  1 

50 

116 

9 

95 

59 

140 

626 

11 

9 

6 

18 

6 

800 

51 

107 

96 

65 

141 

644 

18 

7 

779 

21 

52 

99 

97 

72 

7 

142 

662 

in 

8 

758 

2  1 

53 

91 

98 

79 

7 

H3 

681 

J9 
18 

9 

737 

1  1 

54 

83 

99 

86 

1 

144 

699 

I  n 

10 

717 

2O 

55 

76 

7 

IOO 

94 

H5 

718 

J9 

20 

T 

8 

ig 

ii 

697 

56 

69 

i 

IOI 

102 

146 

737 

12 

678 

'9 

57 

62 

7 

102 

110 

147 

756 

'9 

13 

658 

20 

58 

56 

6 

103 

118 

148 

776 

20 

H 

638 

20 

59 

50 

104 

127 

9 

149 

795 

19 

15 

619 

19 

60 

44 

105 

136 

9 

150 

815 

2O 

16 

600 

19 

61 

39 

5 

1  06 

145 

9 

I5I 

835 

20 

17 

581 

'9 

62 

34 

5 

107 

155 

10 

I52 

855 

20 

18 

563 

18 

63 

29 

5 

108 

165 

IO 

153 

875 

2O 

19 

544 

19 

64 

25 

4 

109 

'75 

IO 

154 

896 

21 

20 

526 

18 

65 

21 

4 

I  IO 

1  86 

1  1 

155 

916 

90 

21 

508 

18 

66 

17 

4 

ii  i 

197 

II 

I56 

936 

20 

22 

491 

'7 

67 

H  ' 

3 

I  12 

208 

II 

157 

957 

2  1 

23 

473 

18 

68 

ii 

3 

I  13 

220 

12 

I58 

978 

1  1 

24 

456 

17 

69 

8 

3 

114 

232 

12 

159 

999 

21 

25 

439 

17 

70 

6 

2 

115 

244 

12 

1  60 

1020 

1  1 

26 

422 

17 

7i 

4 

2 

116 

256 

12 

161 

1041 

21 

27 

406 

16 

72 

3 

i 

117 

269 

i3 

162 

1062 

21 

28 

390 

16 

73 

2 

i 

118 

282 

l3 

•} 

163 

1084 

22 

29 

374 

16 

e 

74 

I 

i 

119 

295 

i3 
-3 

164 

1105 

21 

30 

359 

i5 

75 

0 

o 

1  20 

308 

1  3 

165 

1127 

22 

i5 

o 

14 

22 

31 

344 

76 

0 

121 

322 

1  66 

II49 

32 

329 

i5 

77 

o 

o 

122, 

335 

i3 

167 

II7I 

11 

33 

14 

78 

o 

o 

123 

349 

1  4 

168 

I  192 

1  \ 

34 

301 

14 

79 

I 

I 

124 

364 

i5 

169 

1214 

11 

35 

287 

14 

80 

2 

I 

I25 

378 

14 

170 

1236 

11 

14 

2 

i5 

11 

36 

273 

_  o 

81 

4 

126 

393 

ii 

171 

1253 

11 

37 

260 

IJ 

.0 

82 

6 

2 

I27 

408 

1  3 

172 

1280 

1  1 

38 

247 

13 
l3 

83 

8 

2 

128 

423 

16 

X73 

1301 

11 

39 

234 

12 

84 

10 

3 

129 

439 

16 

174  • 

1323 

11 

40 

222 

85 

13 

130 

455 

*75 

*345 

12 

3 

16 

11 

41 

2IO 

86 

16 

*3r 

47  * 

176 

1367 

42 

198 

12 

87 

20 

4 

132 

487 

16 

177 

1389 

22 

22 

43 

I87 

88 

24 

. 

133 

504 

'7 

178 

141  1 

22 

44 

I76 

89 

28 

521 

7 

179 

H33 

22 

45 

I65 

90 

32 

'35 

538 

'7 

1  80 

H55 

[42] 


TABLE  VII.—  CONTINUED. 

Perturbations  of  the  Logarithm  of  the  Radius  Vector. 

Argument  5.  —  Conckided. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

180° 

1455 

225° 

2317 

270° 

2548 

5 

315° 

1945 

21 

181 

H77 

22 

2  2 

226 

233r 

i3 

271 

2543 

5 

316 

1924 

20 

182 

1499 

227 

2344 

,  •} 

272 

2538 

6 

1»7 

1904 

21 

183 

1521 

22 

228 

2357 

1  O 

i3 

273 

2532 

6 

3i8 

1883 

22 

184 

J543 

22 

229 

2370 

I  2 

274 

2526 

6 

3i9 

1861  . 

21 

185 

1565 

22 

230 

2382 

275 

2520 

320 

1840 

22 

12 

7 

22 

1  86 

1587 

231 

2394 

276 

25X3 

0 

321 

1818 

2  2 

187 

1609 

22 

232 

2406 

I  2 

277 

2505 

o 
8 

322 

1796 

22 

1  88 

1630 

21 

233 

2417 

1  1 

278 

2497 

g 

323 

1774 

22 

189 

1652 

22 

234 

2428 

279 

2489 

324 

1752 

22 

190 

1673 

21 

235 

2439 

1  1 

280 

2480 

9 

325 

1730 

21 

10 

g 

22 

191 

1694 

236 

2449 

281 

2471 

326 

1708 

192 

1716 

22 

237 

2459 

JO 

282 

2462 

9 

327 

1686 

22 
Oo 

*93 

X737 

2  1 

238 

2469 

I  O 

283 

2452 

IO 

328 

1663 

2-J 

194 

1758 

21 

239 

2478 

9 

284 

2442 

IO 

329 

1641 

22 
9Q 

*95 

1779 

2  1 

240 

2487 

9 

285 

243  i 

1  1 

33° 

1618 

3w 

21 

8 

11 

23 

196 

1800 

241 

2495 

286 

2420 

331 

'595 

_Q 

197 

1820 

2O 

242 

2503 

287 

2408 

12 

•  332 

1572 

2s> 

_  •) 

198 

1841 

21 

243 

2510 

7 

288 

2396 

12 

333 

!549 

2J 
_  •j 

199  [  1861 

20 

244 

2517 

7 

289 

2384 

12 

334 

1526 

2o 

nt 

200 

1881 

2O 

245 

2524 

7 

290 

2371 

l3 

335 

«5°3 

20 

2OI 

1901 

20 

246 

2530 

6 

291 

2358 

13 

336 

1480 

23 

202 

1921 

20 

247 

2536 

6 

292 

2345 

i3 

337 

1456 

24 

ol 

203 

1941 

2O 

248 

2541 

293 

2331 

14 

338 

H33 

U 

204 

1961 

20 

249 

2546 

5 

294 

2317 

14 

339 

1409 

24 

0Q 

205 

1980 

19 

250 

2551 

295 

2302 

i5 

34° 

1386 

2J 

2O6 

1999 

19 

251 

2555 

4 

296 

2287 

i5 

34i 

1363 

23 
,,-J 

207 

2018 

'9 

252 

2559 

4 

297 

2272 

i5 

342 

134° 

£\J 

208 

2037 

»9 

253 

2562 

3 

298 

2256 

16 

343 

1316 

24 
ol 

209 

2056 

19 

T» 

254 

2565 

299 

2240 

16 

344 

1293 

2j 
23 

2IO 

2074 

I  o 

255 

2567 

2 

300 

2224 

16 

345 

1270 

21  I 

2092 

18 
18 

256 

2569 

2 

w  o 

301 

2207 

17 

346 

1247 

23 
23 

212 

21  IO 

257 

2571 

302 

2190 

ll 

347 

1224 

2I3 

2127 

!? 

258 

3572 

I 

3°3 

2173 

17 

348 

1200 

24 

rt  Q 

2I4 

2144 

17 

259 

2572 

O 

3°4 

2155 

'  18 

349 

U77 

2o 

nl 

215 

2161 

17 

260 

2572 

O 

3°5 

2137 

18 

350 

1154 

23 

216 

2178 

17 

261 

2571 

I 

306 

2119 

18 

35i 

1131 

23 
•j 

217 

2195 

17 

262 

2570 

I 

307 

2IOI 

18 

352 

1108 

23 

t\  T 

218 

2211 

16 

263 

2569 

I 

308 

2O82 

'9 

353 

1085 

2o 

219 

2227 

16 
/• 

264 

2567 

2 

3°9 

2063 

»9 

354 

1063 

22 

nl 

22O 

2243 

IO 

265 

2565 

2 

310 

2044 

J9 

355 

1040 

2o 

221 

2258 

i5 

266 

2562 

3 

3U 

2025 

19 

356 

1018 

22 
_  -5 

222 

2273 

i5 

267 

2559 

3 

312 

2OO5 

20 

357 

995 

2o 

223 

2288 

i5 

268 

2556 

3 

313 

I985 

20 

358 

973 

22 

224 

Z3°3 

i5 

269 

2552 

4 

3H 

1965 

20 

359 

95i 

22 

225 

2317 

U 

270 

2548 

4 

3i5 

1945 

20 

360 

929 

22 

[43] 


TABLE  VII.  —  CONTINUED. 

Perturbations  of  the  Logarithm  of  the  Radius  Vector. 

Arguments  6  to  12,  inclufive. 

Arg. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

0° 
IO 
20 

3° 

40 

230 
231 

227 
218 
207 

i 

~4 

9 
ii 
i5 

46 
52 

57 
61 

65 

6 

5 
4 
4 
3 

79 
62 
46 
32 

20 

17 
16 

14 

12 

9 

354 
328 

299 
266 
231 

26 
29 

33 
35 
36 

9 
16 

21 
26 
30 

7 
5 
5 
4 
3 

420 

392 
360 

323 
283 

28 

32 

37 

4o 
4i 

40 

27 

15 

7 

2 

i3 

12 

8 
5 

2 

50' 
60 
70 

192 
174 
155 

18 
19 

20 

68 

70 
70 

2 
0 

Q 

II 

4 
i 

7 
3 
i 

'95 

1  60 
125 

35 
35 

32 

33 
37 
41 

4 
4 
3 

242 
201 

161 

4i 
4o 
38 

0 

I 

6 

I 

5 

8 

80 

90 

135 
"5 

20 

70 
69 

I 

0 

3 

3 

93 

65 

28 

44 
48 

4 

123 

88 

35 

H 
25 

ii 

21 

3 

5 

24 

4 

3o 

i3 

IOO 

no 
1  20 

94 

75 
57 

19 

18 
16 

66 
63 
59 

3 
4 
5 

8 

17 
28 

9 
ii 

14 

22 

9 

19 
i3 

1 

52 
57 
63 

5 
6 

58 

34 
16 

24 

18 
ii 

38 
54 

71 

16 

17 
18 

130 
140 
150 
1  60 

28 

17 
9 

i3 
ii 

8 
6 

54 
48 
43 
37 

6 
5 
6 

7 

42 
57 
74 
9' 

i5 

17 
17 
18 

2 

I 

7 
19 

i 

12 

18 

70 

76 
82 

87 

6 
6 
5 
4 

5 
i 

4 
15 

4 
3 

ii 

89 
108 
128 
146 

19 

20 

18 
18 

170 
1  80 

3 
o 

3 

30 
24 

6 

109 

127 

18 

37 
60 

23 

94 

3 

32 
56 

24 

164 
1  80 

16 

0 

5 

17 

27 

i 

29 

i3 

190 

200 

o 
3 

~3 
6 

'9 

H 

5 
5 

144 
1  60 

16 

14 

87 
118 

3i 
33 

95 
93 

2 

3 

-85 
118 

33 
37 

193 

205 

12 

8 

2IO 

22O 

9 

8 
ii 

9 

5 

4 

2 

174 
1  86 

12 

9 

185 

34 
35 

90 
85 

5 

8 

'55 
'95 

4o 
4o 

213 
218 

a  5 

2 

230 
240 
250 
260 

28 

57 
74 

i3 
16 

17 
20 

3 
i 

o 
o 

2 
I 
O 
2 

195 

202 
205 
206 

7 
3 
i 
,3 

220 

255 
288 

319 

35 
33 
3i 
28 

77 
68 

58 
47 

9 

10 

ii 

IO 

235 
275 
3H 
35^ 

4o 
39 

37 
33 

220 
219 
214 
206 

I 

5 
8 
n 

270 

94 

2 

203 

347 

37 

384 

195 

20 

2 

5 

22 

ii 

29 

i3 

280 
290 

114 

134 

20 
20 

4 

7 

3 
4 

198 
189 

9 
ii 

369 
386 

17 

i3 

26 
17 

9 

8 

413 

436 

23 

18 

182 
1  66 

16 
17 

3OO 
310 

154 

19 

18 

1  1 
16 

5 
6 

I78 
164 

14 
i5 

399 
406 

7 
i 

9 

3 

6 
3 

454 
465 

ii 
5 

149 
I3I 

18 
19 

:    32O 
330 
340 

35° 
360 

191 

206 
218 
226 

230 

i5 

12 

8 
4 

22 
28 

34 

40 

46 

6 
6 
6 
6 

149 
132 

"5 

97 
79 

17 
17 
18 
18 

407 
402 

392 
376 

354 

10 

a 

21 

o 
o 

2 

5 
9 

o 

2 

3 
4 

470 
467 

458 
442 
420 

9 
16 

22 

112 

92 

74 
56 
40 

20 

18 

18 
16 

[44] 


TABLE  VII.  —  CONTINUED. 

Perturbations  of  the  Logarithm  of  the  Radius  Vector. 

Arguments  13   to    21,  inclufive. 

Arg. 

13. 

14. 

15. 

16. 

17. 

18. 

19. 

20. 

21. 

o 
0 

66 

i5 

45 

14 

218 

7 

23 

16 

13 

91 

3 

16 

44 

13 

10 

20 

51 

38 

i3 

12 

59 

75 

16 
16 

225 
229 

/ 

4 

Q 

39 
56 

17 

8 
5 

94 
94 

o 
i 

2O 
24 

44 
42 

15 

18 

3° 
40 

26 
16 

10 

Q 

1  06 

i5 

229 
228 

I 

73 
89 

16 

3 
3 

93 
91 

2 

27 
31 

40 
38 

21 

23 

5° 

8 

O 
K 

122 

226 

2 

101 

12 

4 

87 

A 

35 

35 

26 

60 

3 

%j 

3 

136 

i3 

226 

O 
I 

I  IO 

9 
4 

7 

81 

U 

7 

38 

32 

28 

70 

o 

I49 

227 

2 

114 

10 

74 

40 

28 

29 

80 

o 

0 

3 

161 

1  2 

229 

3 

114 

o 

13 

67 

7 

42 

25 

30 

90 

3 

170 

9 

232 

no 

16 

58 

9 

44 

21 

31 

6 

7 

4 

7 

9 

100 

9 

8 

177 

236 

3 

103 

18 

49 

g 

46 

17 

32 

IJO 

17 

IO 

181 

j 

239 

96 

7 

19 

41 

g 

45 

13 

31 

120 

27 

1  2 

182 

J 

240 

2 

89 

7 
6 

19 

33 

g 

45 

IO 

31 

I30 
140 

39 

53 

14 
i5 

181 

177 

4 

7 

238 
231 

7 
ii 

83 
79 

4 

0 

18 

17 

25 
18 

7 
6 

43 

7 
4 

3° 
28 

150 

68 

i5 

170 

220 

16 

79 

2 

15 

12 

5 

39 

2 

26 

I  60 

83 

16 

161 

9 
ii 

204 

23 

81 

6 

13 

7 

3 

37 

I 

24 

170 

99 

i5 

150 

i3 

181 

26 

87 

7 

n 

4 

3 

33 

0 

22 

I  80 

114 

137 

155 

94 

10 

i 

30 

O 

19 

i5 

14 

3o 

8 

i 

190 

129 

i3 

123 

16 

125 

3o 

IO2 

7 

9 

o 

o 

26 

o 

17 

2OO 

142 

12 

107 

16 

95 

3o 

109 

6 

7 

0 

i 

22 

2 

H 

210 
22O 

'54 
164 

IO 

g 

91 

76 

i5 
16 

65 

40 

25 
2  T 

"5 

117 

2 

J 

6 

5 

i 

4 

3 
3 

15 

4 
6 

n 

9 

230 

240 

172 
177 

5 
3 

60 
46 

14 
i3 

19 
6 

i3 
5 

116 
iii 

5 

'     IO 

5 
6 

7 

12 

5 
5 

II 

8 

9 

12 

6 

4 

250 

1  80 

33 

1  2 

i 

3 

101 

I  2 

8 

17 

6 

6 

16 

3 

260 

1  80 

—o 

21 

9 

4 

ii 

89 

16 

10 

23 

6 

4 

19 

2 

270 

177 

12 

15 

73 

15 

29 

2 

23 

I 

6 

7 

19 

17 

8 

280 

171 

8 

5 

34 

23 

56 

17 

37 

O 

27 

O 

290 

163 

10 

I 

I 

57 

28 

39 

J7 
16 

21 

44 

7 
8 

I 

31 

I 

300 

1  53 

O 

85 

23 

24 

52 

0 

I 

34 

I 

3IO 

141 

1  2 

I 

I 

/ 

114 

29 

oR 

ii 

1  2 

0 

26 

60 

o 

g 

3 

37 

2 

32O 
330 

127 

112 

i5 
i5 

5 

12 

4 

7 

142 
1  68 

40 
26 
21 

3 
o 

o 

3 
3 

26 
24 

68 

75 

7 

5 
7 

40 
42 

4 
6 

340 

97 

16 

21 

9 
I  i 

189 

3 

g 

21 

82 

5 

9 

43 

8 

35° 
360 

81 
66 

i5 

32 

45 

i3 

206 
218 

12 

n 

23 

12 

17 
13 

87 

4 

13 
16 

44 
44 

IO 

13 

[45] 


TABLE  VIL  —  CONCLUDED. 

Perturbations  of  the  Logarithm  of  the  Radius  Vector. 

Arguments  22  to  37,  inclufive. 

Are 

22. 

23. 

24. 

25. 

26. 

27. 

?8 

W 

30 

31. 

32. 

33. 

34. 

35 

36 

37 

0° 

12 

22 

26 

35 

6 

7 

8 

10 

0 

7 

1  1 

5 

6 

3 

o 

3 

10 

15 

25 

29 

3° 

7 

5 

8 

10 

I 

9 

12 

6 

7 

3 

i 

4 

20 

17 

28 

31 

24 

9 

3 

7 

10 

2 

10 

'3 

7 

8 

2 

i 

5 

3° 

19 

31 

33 

19 

ii 

i 

7 

10 

3 

1  1 

H 

7 

9 

2 

2 

6 

40 

21 

33 

35 

H 

13 

o 

7 

10 

4 

12 

15 

8 

10 

I 

2 

7 

50 

22 

35 

36 

9 

H 

0 

6 

10 

6 

13 

'5 

9 

10 

I 

3 

8 

60 

24 

37 

36 

6 

16 

0 

5 

9 

8 

'3 

15 

9 

1  1 

0 

4 

9 

70 

25 

38 

36 

3 

17 

I 

5 

9 

10 

H 

16 

9 

12 

O 

4 

10 

80 

25 

38 

35 

i 

'9 

2 

4 

8 

13 

H 

'5 

10 

12 

0 

5 

1  1 

90 

26 

38 

34 

0 

20 

3 

3 

7 

15 

H 

'5 

10 

12 

o 

6 

n 

IOO 

26 

37 

32 

0 

21 

5 

3 

7 

'7 

H 

'5 

10 

12 

o 

6 

12 

no 

25 

36 

3° 

i 

21 

8 

2 

6 

'9 

H 

H 

9 

12 

0 

7 

12 

120 

24 

34 

28 

2 

22 

1  1 

2 

5 

21 

13 

13 

9 

II 

o 

7 

12 

I30 

23 

32 

25 

5 

21 

H 

I 

4 

23 

12 

12 

8 

I  I 

o 

8 

12 

140 

22 

29 

22 

9 

21 

17 

I 

3 

24 

I  I 

10 

8 

10 

I 

8 

12 

150 

20 

26 

19 

*3 

20 

20 

O 

2 

25 

10 

9 

7 

9 

I 

8 

I  I 

I  60 

18 

23 

15 

18 

'9 

23 

0 

I 

26 

9 

8 

6 

8 

2 

8 

10 

170 

16 

20 

12 

23 

18 

26 

O 

I 

26 

8 

6 

6 

7 

2 

8 

10 

I  80 

«4 

16 

10 

29 

16 

29 

o 

0 

26 

7 

5 

5 

6 

3 

8 

9 

I9O 

ii 

13 

7 

34 

15 

31 

o 

O 

25 

5 

4 

4 

5 

3 

7 

8 

200 

9 

10 

5 

40 

'3 

33 

I 

0 

24 

4 

3 

3 

4 

4 

7 

7 

2IO 

7 

7 

3 

45 

1  1 

35 

I 

o 

23 

3 

2 

3 

3 

4 

6 

6 

22O 

5 

*5 

i 

50 

9 

36 

I 

o 

22 

2 

2 

2 

5 

6 

5 

230 

4 

3 

o 

55 

8 

36 

2 

0 

2O 

I 

I 

2 

5 

5 

4 

240 

2 

i 

o 

58 

6 

36 

3 

I 

18 

I 

I 

I 

6 

4 

3 

250 

I 

o 

0 

61 

5 

35 

3 

I 

16 

0 

0 

I 

O 

6 

4 

2 

26o 

I 

o 

I 

63 

3 

34 

4 

2 

13 

O 

O 

O 

6 

3 

I 

270 

0 

o 

2 

64 

2 

33 

5 

3 

n 

o 

0 

0 

6 

2 

I 

280 

o 

I 

4 

64 

I 

3i 

5 

3 

9 

o 

I 

0 

o 

6 

2 

O 

290 

I 

2 

6 

63 

I 

28 

6 

4 

7 

o 

2 

I 

0 

6 

I 

0 

3OO 

2 

4 

8 

62 

0 

25 

6 

5 

5 

I 

3 

I 

I 

6 

I 

o 

3IO 

3 

6 

ii 

59 

I 

22 

7 

6 

3 

2 

4 

2 

I 

6 

O 

o 

32O 

4 

9 

H 

55 

I 

19 

7 

7 

2 

3 

6 

2 

2 

5 

0 

0 

33° 

6 

12 

17 

5i 

2 

16 

8 

8 

I 

4 

7 

3 

3 

5 

O 

I 

340 

8 

15 

21 

46 

3 

'3 

8 

9 

O 

5 

8 

4 

4 

4 

o 

2 

35° 

10 

18 

24 

4' 

4 

10 

8 

9 

O 

6 

10 

4 

5 

4 

0 

2 

360 

12 

22 

26 

35 

6 

7 

8 

10 

o 

7 

n 

5 

6 

3 

o 

3 

\ 

[46] 


TABLE  VIII. 

Terms  in  S  log.  r  to  be  Multiplied  by  t.      \ 

Argument    10.  _____ 

0° 

I 

2 

-  41.88 

45-H 
48-38 

3.26 

3.24 

45° 
46 
47 

-146.68 

H7.7I 
148.68 

i.o3 
0.97 

9°° 
91 
92 

—  14I.6l 

140.52 
139.40 

1.09 

1.  12 

T      T  / 

135° 
136 
137 

-68.96 
66.95 
64-94 

2.O1 
2.01 
2.o3 

3 

51.60 

3rirt 
.22 

o   T  _ 

48 

149.60 

0.92 

n  RA 

93 

138.26 

I.I4 

1.18 

138 

62.91 

2.o5 

4 

54-79 

o.IQ 

49 

1  50.46 

u.ou 
0.80 

94 

137.08 

1  .2  1 

139 

60.86 

2.04 

5 

57-95 

•j  .  I  O 

5° 

151.26 

95 

135.87 

140 

58.82 

3.i4 

0.75 

1.24 

2.06 

6 

7 
8 

—  61.09 

64-19 
67.27 

3.IQ 

3.o8 
3.o4 

5i 

52 
53 

—  152.01 
152.70 
153.33 

0.69 
o.63  ' 
0.57 

96 

97 
98 

-134-63 
133-37 
132.08 

1.26 

1.29 

i.33 

141 
142 
H3 

-56.76 

54-69 
52.61 

2.Q7 
2.08 
2.08 

9 

70.31 

3.oi 

54 

153-9° 

o.5i 

99 

130-75 

1.35 

144 

5°-53 

2.09 

10 

73-32 

55 

154.41 

100 

129.40 

H5 

48.44 

2.97 

o.45 

i.38 

2.Q9 

1  1 

-  76.29 

2.g3 

56 

—  154.86 

o.3o 

101 

—  128.02 

1.41 

146 

-46.35 

2.  II 

12 

79.22 

2.8o 

57 

155-25 

^"-'y 
o.34 

IO2 

I26.6l 

1.43 

H7 

44.24 

2.  II 

13 

82.11 

2.85 

58 

155-59 

0.28 

103 

125.18 

1.43 

148 

42.13 

2.12 

H 

84.96 

59 

155.87 

O.23 

104 

123--73 

I  Al 

H9 

40.01 

2.12 

15 

87.77 

2.76 

60 

156.10 

0.18 

105 

122.26 

1.4  _ 
1.49 

150 

37.89 

2.13 

16 

-  9°-53 

61 

—  156.28 

1  06 

-120.77 

1SI 

-35.76 

2.13 

17 

93-25 

2.72 

62 

156.40 

O.  I  2 
O.o8 

107 

119.25 

1  .32 

152 

33-63 

2.14 

18 
19 

95.92 
98.53 

2.67 
2.61 

63 
64 

156.48 
156-51 

o.o3 

108 
109 

117.70 
1  16.13 

1  .  33 

i.57 

153 
154 

29-35 

2.14 

2.l5 

20 

101.10 

2.  37 

65 

156.49 

I  10 

II4-54 

9 

155 

27.20 

_       r 

2.52 

0.07 

1.61 

2.13 

21 

—  103.62 

o   Xi 

66 

-156.42 

O  I  2 

iii 

-112.93 

1.63 

156 

-25.05 

2.l5 

22 

106.09 

2.47 
2/  _ 

67 

156.30 

I  12 

1  1  1.30 

157 

22.90 

2.16 

23 

108.50 

•  41 

2.35 

68 

156-13 

0.17 
O.22 

H3 

109.65 

1.67 

158 

20.74 

2.l5 

24 

110.85 

0    ft 

69 

155.91 

I  14 

107.98 

1  •    / 

159 

18.59 

2.16 

25 

1  1  3.16 

4.O  1 

70 

155.65 

I  15 

106.28 

1.70 

1  60 

16.43 

2.24 

O.32 

1.72 

2.17 

26 

-115.40 

7i 

-I55-33 

o  35 

116 

—  104.56 

I    73 

161 

—  14.26 

2.16 

27 
28 
29 

117.59 

H9.73 
121.81 

2.19 
2.14 

2.08 

72 
73 
74 

154.98 
154.59 

154-14 

o.3g 
o.45 

117 
118 
119 

102.83 
101.09 
99-32 

1.70 
1-74 
'•77 

162 
163 

164 

12.  IO 
9.94 

7.78 

2.16 

2.16    . 
2.16 

3° 

123.82 

2.QI 

1.95 

75 

153.65 

0.49 
o.53 

1  20 

97-53 

1.79 
i.  80 

165 

5.62 

2.16 

32 

-125.77 
127.66 

1.89 

i    fio 

76 

77 

-153.12 

152.55 

0.57 

121 

122 

-  95-73 
93-9i 

1.82 

166 
167 

346 

2.16 

2.l5 

33 

129.48 

1  .02 

78 

15L93 

O.O2 
^  AA 

I23 

92.07 

T  RA 

168 

+     0.85 

2.16 

34 

131.25 

1.77 

79 

151.27 

Q.OO 

124 

90.21 

l  .00 

169 

3.OI 

2.17 

3t5 

132.96 

i.65 

80 

150.58 

0.69 
O.73 

125 

88.35 

1.88 

170 

5.I8 

2.l5 

36 

-134.61 

t     Kr. 

81 

-149-85 

126 

-  86.47 

171 

+   7-33 

2.l5 

37 

136.20 

I  .09 

82 

149.08 

0.77 

OQn 

I27 

84.57 

i  .90 

172 

9.48 

2.l3 

38 

137-72 

1.52 

1.47 

83 

148.26 

,O2 

o.85 

128 

82.67 

i  .90 
1.92 

J73 

ii.  61 

2.14 

39 

i39-!9 

•••»! 

I/  T 

84 

147-41 

r>  88 

I29 

80.75 

1  74 

1  3-75 

2.13 

40 

140.60 

•  41 

85 

i46-53 

u.oo 

I30 

78.82 

1.9 

175 

15.88 

n     w  *> 

i.34 

0.91 

i.95 

2.1  j 

42 

-141.94 
143.21 

1.27 

86 

87 

-145-62 
H4.67 

0.95 

131 

132 

-  76.87 
.  74.9i 

1.96 

176 

177 

+  18.01 
20.14 

2.13 
2.l3 

43 

144.42 

1.  21 

-        T  A 

88 

143.68 

0.99 

133 

72.94 

1.97 

I    nR 

178 

22.27 

2.12 

44 

145.58 

1  .  10 

89 

142.67 

1  .01 

134 

70.96 

1  .90 

179 

24-39 

2.  II 

45 

146.68 

I.IO 

90 

141.61 

1  .06 

135 

68.96 

2.00 

180 

26.50 

[47] 


TABLE  VIII.  —  CONCLUDED. 

Terms  in  §  log.  r  to  be  Multiplied  by  t. 

Argument  1  0.  —  Concluded. 

1  80° 

+  26.50 

225° 

+  107.89 

T   3-7 

270° 

+  140.70 

3'5° 

+  92-36 

181 

28.60 

2.  IQ 

226 

109.26 

1.07 

271 

140.64 

O.OO 

3'6 

90.15 

2.21 

182 

30.69 

2.09 

227 

1  1  0.6  1 

i.35 

272 

'4°-53 

O.I  I 

3'7 

87.89 

2.26 

n  1  T 

183 

32.78 

2.09 

228 

111.93 

1.32 

273 

140.38 

o.  1  5 

318 

85.58 

2.JI 

184 

34.85 

2.07 

229 

113-23 

i.Jo 

274 

140.19 

o.  19 

3'9 

83.21 

2.36 

185 

36.92 

2.07 

230 

114.50 

1.27 

275 

139.96 

O.23 

320 

80.80 

2.41 

2.06 

1.24 

0.27 

2.45 

186 

+  38.98 

2.o5 

23I 

+  "5.74 

1.22 

276 

+  139.69 

O  32 

321 

+  78.35 

2  5o 

187 

41.03 

232 

116.96 

277 

'39-37 

322 

75.85 

188 

43.06 

2.o3 
2.o3 

233 

118.16 

1.  2O 

1.16 

278 

139.01 

o  4o 

323 

73-3' 

2.54 

189 
190 

45.09 
47.11 

2.02 

234 

235 

119.32 
120.46 

1.  14 

279 
280 

138.61 
138.16 

0.45 

324 
325 

70.72 
68.08 

2.64 

2.OO 

1.  12 

0.49 

2.68 

191 

+  49-11 

236 

+  121.58 

281 

+  137.67 

326 

+  65.40 

192 
193 

51.11 

53-'o 

2.OO 
1-99 

237 
238 

122.67 

'23.73 

1.09 
1.  06 

i.o3 

282 
283 

137.13 

'36.55 

o.58 
062 

327 

328 

62.68 
59-92 

2.72 
2.76 

0  fin 

194 
'95 

55-07 
57-03 

1.97 
1.96 

239 
240 

124.76 
125.76 

1.  00 

284 
285 

'35-93 
135.26 

0.67 

329 

330 

57.12 
54-27 

2.OO 

2.85 

I.gS 

0.97 

0.72 

2.88 

196 
197 

+  58.98 
60.91 

1.93 

241 

242 

+  126.73 
127.68 

0.95 

286 
287 

+  '34-54 
133.77 

0.77 

r>  Si 

33' 

332 

+  5'.39 
48.47 

2.92 

198 

62.82 

I.9I 

243 

128.59 

0.91 

0.88 

288 

132.96 

U.Ol 

o.85 

333 

45-5' 

2.96 

199 

6473 

I.gl 

I  8r> 

244 

129.47 

289 

132.11 

334 

42.52 

2.99 

3.02 

200 

66.62 

I.»9 

245 

130.32 

0. 

290 

131.21 

0.90 

335 

39-50 

1.87 

0.82 

0.95 

3.06 

2OI 

+  68.49 

246 

+  131.14- 

291 

+  130.26 

336 

+  36.44 

2O2 

70.35 

i  8/ 

247 

0.79 

292 

129.26 

i  .00 

337 

33-35 

3.09 
Iff 

203 

72.19 

i  .04 
1.82 

248 

132.69 

O.7O 

0.73 

293 

128.20 

i  .00 

1.  10 

338 

30.24 

O.  I  I 

3.i5 

204 

74.01 

1.81 

249 

'33.42 

i 
0.69 

294 

127.10 

339 

27.09 

•3.17 

205 

75.82 

250 

134.11 

295 

125.95 

34° 

23.92 

/ 

1.79 

0.66 

I.2O 

3.19 

2O6 

+  77-6i 

1.77 

251 

+  '3477 

o.63 

296 

+  124.75 

1.24 

34' 

+  20.73 

3.21 

207 

79.38 

252 

'35-40 

297 

123.51 

i.3o 

342 

17.52 

3  23 

208 

81.14 

In  / 

253 

136.00 

O.OO 

298 

122.21 

343 

14.29 

209 
2IO 

82.88 
84.60 

•74 
1-72 

254 
255 

136.56 
137.09 

o.53 

299 
300 

120.86 
1  19.46 

1.40 

344 
345 

1  1.04 
I'll 

o.  2D 
3.27 

1.70 

o.5o 

1.45 

3.29 

211 

+  86.30 

1.68 

256 

+  '37-59 

0.46 

301 

+  118.01 

i.Si 

346 

+  4.48 

3.3i 

212 

87.98 

1.65 

257 

138.05 

302 

1  16.50 

i  55 

347 

1.17 

213 

89.63 

1.64 

258 

138.46 

0.39 

303 

114.95 

1.61 

348 

—  2.14 

3.3i 

214 

91.27 

1.62 

259 

138.85 

o.36 

3°4 

"3-34 

i.65 

349 

5-45 

3.3i 

215 

92.89 

260 

139.21 

305 

1  11.69 

350 

8.76 

i.  60 

0.32 

1.71 

3.32 

216 

+  94-49 

i.58 

261 

+  '39-53 

n  oft 

306 

+  109.98 

35' 

—  1  2.08 

*3.o2 

217 

96.07 

i.56 

262 

139.81 

U.  £.0 

3°7 

108.23 

1.81 

352 

15.40 

3  33 

218 

97.63 

263 

140.05 

o.  24 

308 

106.42 

1.86  ' 

353 

'8-73 

-j  -5-3 

219 

99.17 

264 

140.26 

0.  21 

3°9 

104.56 

354 

22.06 

O.  O  J 

7  3*3 

22O 

1  00.68 

i 

265 

'40.43 

0.17 

310 

102.66 

i  .90 

355 

25-39 

O.OO 

1.49 

o.i3 

1.96 

3.3a 

221 

+  102.17 

*  /-. 

266 

+  140.56 

3" 

+  100.70 

356 

—  28.71 

222 
223 

103.64 
105.08 

'•47 
1-44 

267 
268 

140.66 

140.71 

O.  IO 

o.o5 

312 
3'3 

98.69 
96.63 

2.OI 
2.06 

357 
358 

32.02 
35.32 

3.3o 

224 

106.49 

1.41 
i.4o 

269 

140.72 

O.OI 
O.O2 

3'4 

94.52 

2  .  1  1 
2.l6 

359 

38.60 

3.28 

225 

107.89 

270 

140.70 

92.36 

360 

41.88 

[48] 


TABLE    IX.—  CONTINUED. 

Perturbations  of  the  Co-ordinate  £. 

Argument  1.                                                                            Argument  2. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

0° 

281.4 

o.3 

1  80° 

277.6 

2.2 

0° 

213-5 

2.7 

1  80° 

124.1 

0.7 

5 

283.2 

0.4 

185 

265.3 

2.6 

5 

199.4 

2.9 

I85 

120.5 

0.7 

10 

285.5 

o.5 

190 

251.1 

3.0 

10 

184.6 

3.o 

190 

II7.O 

o.7 

15 

288.5 

0.6 

195 

235.1 

3.3 

'5 

169.3 

3.i 

'95 

113.6 

0.6 

20 

292.0 

0.7 

200 

2  I  8.0 

3.5 

20 

153-6 

3.2 

200 

III.O 

0.4 

25 

295.7 

0.8 

205 

200.3 

3.5 

25 

I37-7 

3.2 

205 

109.6 

O.I 

3° 

299.6 

0.8 

2IO 

182.6 

3.5 

30 

I2I.8 

3.i 

2IO 

109.6 

0.2 

35 

3°3-4 

0.7 

215 

165.4 

3.3 

35 

106.2 

3.i 

215 

III.  2 

o.5 

40 

307.1 

0.7 

22O 

149.1 

3.1 

40 

91.0 

3.o 

22O 

II4.6 

0.9 

45 

310.2 

o.5 

225 

134-7 

2.7 

45 

76.5 

2.8 

225 

I  20.  1 

i.3 

5o 

3I2-5 

.0.4 

230 

122.  1 

1.1 

5o 

63.0 

2.5 

230 

127.4 

1.6 

55 

313-8 

0.2 

235 

II2.4 

1-7 

55 

,51.0 

1.1 

235 

136.6 

2.0 

.      60 

314.2 

o.i 

240 

105.2 

I.I 

60 

40-5 

1.9 

240 

H7-3 

2.3 

65 

3'3-2 

o.3 

245 

IOI.2 

o.5 

65 

3'-9 

1.5 

245 

159-4 

2.5 

70 

3ii-3 

o.5 

250 

IOO.3 

O.I 

70 

25-3 

I.I 

250 

172.5 

2.7 

75 

308.3 

0.7 

255 

102.7 

0.8 

75 

21.  1 

0.6 

255 

186.3 

2.8 

80 

304-7 

0.8 

260 

107.9 

1.3 

80 

I9.O 

0.2 

260 

2O0.6 

2.8 

85 

300.6 

0.8 

265 

II5.9 

1.8 

85 

19.4 

o3 

265 

214.8 

2.8 

90 

296.5 

0.8 

270 

I26.I 

1.1 

90 

21.9 

0.7 

270 

228.5 

2.7 

95 

292.8 

0.7 

275 

138.4 

2.6 

95 

26.6 

I.I 

275 

241.3 

2.5 

IOO 

289.7 

o.5 

280 

I52.I 

2.8 

IOO 

33-2 

i.5 

280 

253.2 

1.1 

105 

287.4 

0.4 

285 

166.6 

2.9 

105 

41.5 

1.8 

285 

263.7 

1.9 

IIO 

286.1 

O.I 

290 

181.5 

3.o 

no 

50.9 

2.0 

290 

272.5 

1.6 

"5 

286.0 

O.I 

295 

196.5 

2.9 

"5 

61.3 

2.1 

295 

279.4 

1.2 

120 

287.0 

o.3 

30O 

210.8 

2-7 

1  20 

72.1 

1.1 

300 

284.5 

0.8 

125 

289.1 

o.5 

3°5 

224.0 

2.5 

125 

83.0 

2.1 

305 

287.6 

0.4 

130 

291.9 

0.6 

3IO 

235.9 

2.2 

130 

93-4 

2.0 

3IO 

289.0 

O.I 

135 

295.2 

0.7 

315 

246.2 

1-9 

135 

103.0 

1.8 

315 

288.4 

ol 

140 

298.5 

0.6 

320 

254.9 

1.6 

140 

ii  1.6 

1.6 

320 

286.0 

0.7 

H5 

301.4 

o.5 

325 

261.8 

1.2 

H5 

118.7 

1.3 

325 

281.8 

1.0 

150 

303.6 

0.3 

33° 

267.4 

1.0 

150 

124.2 

0.9 

330 

276.0 

i.3 

155 

3°4-3 

0.0 

335 

271.5 

0.7 

155 

128.0 

0.6 

335 

268.7 

1.6 

1  60 

303-4 

0.4 

34° 

274.6 

o.5 

1  60 

130.2 

o.3 

34° 

260.0 

1.9 

165 

300.5 

0.8 

345 

276.9 

0.4 

165 

130.6 

0.0 

345 

250.0 

2.1 

170 

295-3 

i.3 

350 

278.5 

o.3 

170 

129.6 

o.3 

35° 

238.8 

2.3 

175 

287.6 

1.8 

355 

280.0 

o.3 

175 

127.3 

o.5 

355 

226.6 

2.5 

1  80 

277.6 

1.1 

360 

281.4 

o.3   * 

1  80 

124.1 

0.7 

360 

213.5 

2.7 

*.£*  The  Differences  are  calculated  for  i  Degree, 

• 

[49] 


TABLE  IX.—  CONTINUED. 

Perturbations  of  the  Co-ordinate  £. 

Argument  3.                                                                     Argument  4. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

Arg. 

Eq. 

D. 

0° 

9-1 

Q.I 

1  80° 

433-3 

I.O 

0° 

I  20.  1 

5.3 

1  80° 

74.3 

0.7 

5 

5-6 

0-7 

185 

437-6 

0.7 

5 

93-i 

5.3 

185 

74.1 

o.5 

10 

1.6 

0.4 

190 

440.4 

0.4 

10 

67.2 

4-9 

190 

79-o 

1.4 

15 

0.5 

O.I 

'95 

441.6 

O.I 

15 

43-9 

4.4 

195 

87.9 

2.1 

20 

0.9 

~o~3 

200 

44L3 

0.2 

20 

23-4 

3.5 

200 

100.4 

2.6 

25 

3-2 

0.6 

205 

439-1 

0.6 

25 

9.1 

2.2 

205 

114.0 

2-7 

30 

7.0 

0.9 

210 

435-4 

0.9 

3° 

1.2 

Q.8 

2IO 

127.6 

2.6 

35 

12.6 

i.3 

2I5 

430.0 

1.2 

35 

0.6 

0.6 

215 

139.7 

2.1 

40 

19.7 

1.6 

22O 

423-1 

1.5 

40 

7-3 

2.1 

220 

148.9 

i.5 

45 

28.4 

1.9 

225 

414.6 

1.8 

45 

21.6 

3.5 

225 

154.4 

0.7 

50 

38.5 

2.2 

23O 

405.0 

2.1 

5° 

42.7 

4.8 

230 

155-5 

0.2 

55 

50.2 

2.4 

235 

393-5 

2.4 

55 

70.0 

6.0 

235 

152.1 

I.I 

60 

63.0 

2.7 

240 

381.0 

2.6 

60 

102.3 

6.9 

240 

144.7 

1.8 

65 

77.2 

2.9 

245 

367.1 

2.9 

65 

138.6 

7.5 

245 

'3  4-° 

2.4 

70 

92-3 

3.i 

250 

352.3 

3.1 

70 

177.1 

7.8 

250 

121.  1 

2-7 

75 

108.5 

3.3 

255 

336-4 

3.3 

75 

2l6.2 

7-7 

255 

107.3 

2.7 

80 

125.5 

3.5 

260 

3I9-7 

3.4 

80 

254.3 

7.3 

260 

93-9 

2.5 

85 

143.2 

3.6 

265 

302.1 

3.6 

85 

289.6 

6.7 

265 

82.5 

2.0 

90 

161.6 

3.7 

270 

284.0 

3.7 

9° 

320.9 

5.7 

270 

74-3 

1.2 

95 

180.4 

3.8 

275 

265.4 

3.7 

95 

346.8 

4.5 

275 

70.5 

0.3 

IOO 

199.5 

3.8 

280 

246.5 

3.8 

IOO 

366.3 

3.2 

280 

71-5 

0.7 

105 

218.7 

3.8 

285 

227.2 

3.9 

105 

378.6 

i-7 

285 

77.5 

i-7 

no 

237.9 

3.8 

290 

207.9 

3.8 

IIO 

383.1 

O.I 

290 

88.3 

2.6 

"5 

257.0 

3.8 

295 

188.8 

3.8 

"5 

379-6 

T4 

295 

103.3 

3.3 

1  20 

275.8 

3.7 

3OO 

169.8 

3.8 

120 

368.6 

2.9 

300 

121.4 

3.8 

125 

294.2 

3.6 

305 

151.2 

3.7 

125 

350.5 

4.2 

305 

141.2 

3.9 

130 

312.0 

3.5 

310 

133-2 

3.5 

130 

326.5 

5.3 

310 

160.9 

3.8 

!35 

329.1 

3.3 

315 

115.8 

3.4 

135 

297.7 

6.1 

315 

179.2 

3.3 

140 

345-5 

3.2 

32O 

99.3 

3.2 

140 

265.5 

6.6 

320 

194.3 

2.6 

H5 

360.7 

3.o 

325 

83-7 

3.o 

145 

231.6 

6.8 

325 

204.8 

i.5 

150 

375-0 

2-7 

330 

69.0 

2.8 

150 

197.7 

6.6 

330 

209.7 

0.4 

*55 

388.1 

2.5 

335 

55.6 

2.6 

'55 

165.5 

6.1 

335 

208.5 

0.8 

1  60 

400.1 

2.2 

34° 

43-3 

2.3 

1  60 

136.6 

5.3 

34° 

201.2 

2.1 

165 

410.5 

1.9 

345 

32.6 

2.0 

165 

112.  2 

4.3 

345 

187.6 

3.2 

170 

419.6 

i-7 

35° 

23-2 

i-7 

170 

93-4 

3.i 

350 

168.8 

4.2 

»75 

427.3 

1.4 

355 

15.4 

1.4     , 

175 

80.7 

1.9 

355 

145.8 

4-9 

180 

433-3 

I.O 

360 

9-1 

i.i 

1  80 

74-3 

0.7 

360 

I  20.  1 

5.3 

*£*  The  Differences  are  calculated  for  i   Degree. 

• 

[50] 


TABLE  IX.—  CONTINUED. 

Perturbations  of  the  Co-ordinate  £. 

Arguments  9  to  15,  inekifive. 

Arg. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

13. 

14. 

15. 

0° 

64.8 

3.8 

13.6 

3.5 

5-5 

2.1 

17.0 

5-2 

1.8 

2.4 

O.O 

0.6 

14 

32.0 

10 

20 

6  i.o 
56.4 

4.6 
5.o 

I  O.I 

6-9 

3.2 
2.6 

5-3 
5.0 

1.4 

0.7 

14.5 
11.9 

34 
3-3 

O.I 

2.0 

1.6 

0.0 

O.I 

0.7 

37.6 
43.2 

5.6 
5.6 

30 

51.4 

5.3 

4-3 

2.  1 

4.6 

0.3 

94 

4.8 

2.8 

1.2 

I.O 

0.0 

0.0 

48.3 

5.i 

40 

46.1 

5.5 

2.2 

4.2 

0.0 

7.2 

7.6 

3  o 

0.8 

2.0 

0.3 

O.O 

53-° 

4.7 

5° 

40.6 

0.9 

3-7 

O.I 

5.1 

11.5 

0.9 

0.6 

3.1 

0.8 

O.I 

57-1 

4.1 

60 

70 

35-° 
29.6 

5.4 
5.3 

0.2 

°-7 

O.I 

0.8 

3-2 
2.7 

0.3 

0.6 

3-3 
1.8 

16.1 

20.8 

4-7 
A  3 

0.4 

0.2 

4.6 

6.2 

i-S 

2.4 

0.5 

I.I 

60.4 
62.9 

3.3 

2.5 

80 

24-3 

5.o 

I.I 

2.2 

1.2 

0.8 

25.1 

£|.*vJ 

4-0 

O.I 

8.1 

3-5 

1.8 

64.5 

1.6 

n  f\ 

90 

19-3 

2.6 

1.8 

2.0 

0.2 

29.1 

O.O 

9-9 

4-7 

2.7 

65.1 

u.u 

IOO 

14.5 

4.8 

4-7 

2.1 

1-3 

2-9 

0.0 

32.5 

3.4 

O.I 

ii.  8 

5-9 

3-8 

64.7 

0.4 

I  10 

10.4 

4-1 
i  f\ 

74 

2.7 

0.9 

4.0 

O.2 

35-2 

2.7 

o  •} 

O.2 

13-6 

74 

4.9 

63-3 

1.4 

120 

6.9 

O.O 

n    n 

10.6 

3.  2 

0.6 

5-1 

0.9 

37-5 

Z.\J 

1.8 

0.4 

15.4 

8-7 

6.1 

61.0 

2.3 

I30 

4.0 

2-9 

H-3 

'7 

0.3 

6.3 

2.1 

39-3 

1.6 

0.7 

17.1 

IO.O 

7-3 

57-9 

3.i 

140 

1.9 

2.1 
I.I 

18.2 

4.1 

0.2 

7-6 

3-6 

40.9 

1.2 

I.O 

1  8.6 

"•3 

8.6 

53-9 

4.0 

/    /I 

150 

0.8 

o.3 

22.3 

4    ft 

0.0 

8-7 

54 

42.1 

1.3 

14 

19.8 

12.4 

9-7 

49-3 

4.6 

I  60 

0.5 

26.5 

.2 
4_ 

0.0 

9-9 

7-5 

434 

I   2 

1.8 

20.7 

13-5 

10.8 

*44.2 

5.1 

170 

1.2 

0.7 
i  8 

30.5 

.0 

O.O 

I  I.O 

9-9 

44-6 

I   2 

2.2 

214 

14.4 

u.  8 

38.8 

5.4 

I  80 

3.0 

1  .  O 

344 

3.9 

O.I 

11.9 

12.4 

45-8 

2.6 

21.8 

15.0 

12.6 

33-2 

5.6 

3.o 

3.5 

1.2 

5.6 

190 

6.0 

4,, 

37-9 

30 

0.4 

12.6 

14.9 

47.0 

3-0 

21.8 

15.4 

^3-3 

27.6 

2OO 

IO.O 

.0 

/  8 

41.1 

.2 

n    £. 

0.7 

13.3 

17.5 

48.0 

I  .O 
r»  Q 

34 

21.5 

15.5 

13.7 

22.  0 

5.6 

210 

14.8 

4.0 
5.5 

43.7 

2.O 

2.1 

I.O 

13.7 

2O.O 

48.8 

O.o 

0.8 

3-8 

20.8 

15.6 

14.0 

16.8 

5.2 

220 

20.3 

6.3 

45.8 

T     0 

1.4 

14.0 

22.2 

49.6 

4.2 

19.8 

"5-3 

14.0 

12.  1 

4-7 

230 

26.6 

6.7 

47.i 

I.O 

0.6 

1.9 

13.9 

24-3 

50.1 

O.2 

4-5 

18.7 

14.8 

'3-9 

8.1 

4.0 

240 

33.3 

A  n 

47.7 

2.4 

13.7 

26.1 

5°-3 

„  o 

4-7 

17.2 

14.1 

1  3.5 

4.8 

3.3 

250 

40.0 

0-7 

47.6 

O.  I 

2.9 

134 

27.6 

50.0 

O.O 

4.8 

15.6 

13.2 

12.9 

2.3 

2.5 

260 

46.7 

6.7 
6.2 

46-9 

0.7 
i.5 

34 

12.7 

28.6 

49.2 

0. 

4.9 

13.7 

12.  1 

12.2 

0.7 

1.6 

270 

52.9 

454 

3-8 

12.0 

29.2 

47-5 

1-1 

5.0 

11.9 

IO.9 

II.3 

O.I 

0.6 

5.6 

2.1 

2.6 

280 

58.5 

4m 

43-3 

4.2 

II.  I 

29.4 

44-9 

4-9 

IO.O 

9-7 

IO.2 

0.5 

0.4 

290 

63.2 

•1 

40.6 

2.7 

3_ 

4-6 

IO.O 

29.2 

41.2 

3.7 

4.8 

8.2 

8.3 

9.1 

1.9 

1.4 

300 
3IO 

66.9 
69.6 

2.7 

374 
33-7 

.2 

3.7 
•j  n 

5.0 
5-3 

8.9 

7-7 

28.5 
27.3 

36.5 

4.7 
5.4 
6.0 

4.6 

4.3 

6.4 

4-7 

6.9 

5-6 

7.9 

6.7 

4.2 

7-3 

2.3 

320 

70.9 

29.8 

0.9 

5-5 

6-5 

25.8 

25.1 

A,  T 

4.0 

3.2 

4-3 

5-5 

"•3 

4.0 

330 

71.0 

I    .O 

25.7 

4.1 
4.2 

5.6 

5-3 

24.0 

19.0 

O.  I 

5.6 

3.6 

2.O 

3-2 

4-3 

15.9 

4.6 

34° 

70.0 

21.5 

5-6 

4-1 

21.9 

1  3.4 

3-2 

I.I 

2.1 

3-2 

21.0 

5.i 

35° 

67.8 

2.2 

17-5 

4.0 

5-6 

3-° 

19.5 

8-7 

4-7 
i  *; 

2.8 

0.4 

1.2 

2.2 

26.4 

5.4 

360 

64.8 

.Q 

13.6 

•9 

5-5 

2.1      17.0  : 

5-2 

O.D 

2.4 

0.0 

0.6 

1.4 

32.0 

5.6 

[51] 


TABLE  IX.—  CONTINUED. 
Perturbations  of  the  Co-ordinate  £. 
Arguments  16  to  29,  inclufive. 

Arg. 

16. 

17. 

18. 

19. 

20. 

21. 

22. 

23. 

24. 

25. 

26. 

27. 

28. 

29. 

o 

O 

1.9 

7-3 

21.5 

n  n 

O.I 

I.O 

o.o 

10.5 

3-3 

4.2 

0.2 

15-6 

o.o 

5-5 

2.4 

IO 

1.9 

6.1 

28.5 

7.0 
7-5 

o.o 

0.9 

o.o 

9-7 

3-9 

2.6 

0.0 

14.2 

0.0 

5.8 

2O 

1.9 

4-7 

36.0 

7-9 

0.0 

0.7 

0.0 

8.8 

4-5 

'•4 

0.0 

12.7 

O.I 

6.0 

3-9 

3° 

2.O 

3.1 

43-9 

8.0 

0.0 

0.7 

O.I 

7-9 

5.0 

0.5 

O.I 

II.  2 

°>3 

6.1 

4-7 

40 

2.1 

1.6 

51.9 

7  8 

o.o 

•0.6 

O.I 

6.9 

5-5 

0.0 

0-3 

9-5 

0.5 

6.2 

5-5 

5° 

2-3 

0.6 

59-7 

/•" 

1  ") 

O.I 

0.4 

O.2 

5-8 

5-9 

o.o 

0.6 

7.8 

0.8 

6.1 

6-3 

60 

2-5 

o.o 

67.2 

7-j 
6.9 

°-3 

0.4 

0.3 

4-8 

6.2 

0.4 

I.O 

6.2 

i.i 

5-9 

7-2 

70 

2.7 

O.2 

74.1 

0.5 

O.2 

0.4 

3-8 

6-5 

I.I 

1.5 

4.8 

1.4 

5-6 

7-9 

80 

2.8 

0.8 

80.0 

A  8 

0.7 

0.2 

0.5 

2.8 

6.7 

2-3 

2.1 

3-4 

1-7 

5-3 

8.4 

90 

2.9 

1.9 

84.8 

**•<-> 

3.4 

I.O 

O.I 

0.6 

1.9 

6.8 

3-8 

2.8 

2.2 

2.1 

4-9 

8.9 

IOO 

2.9 

3.1 

88.2 

'•3 

O.O 

0.7 

1.2 

6.7 

5-7 

3-5 

1.4 

2-5 

4-5 

9-2 

no 

2.7 

4-3 

90.1 

1.9 
o.3 

1.6 

0.0 

0.8 

0.7 

6.6 

77 

4-3 

0.6 

2.8 

4.0 

9-5 

120 

2.5 

5-4 

90.4 

1.9 

O.O 

0.9 

0.2 

6-4 

I  O.O 

5.0 

0.2 

3.1 

3-5 

9-6 

130 

2.2 

6.1 

89.1 

'' 

2.2 

O.O 

.0 

O.O 

6.1 

12.4 

5.8 

O.O 

3.4 

2.9 

9-5 

140 

1.8 

6-5 

86.3 

A  1 

2-5 

0.0 

.1 

O.O 

5-7 

14.8 

6.5 

0.2 

3.7 

2.4 

9-3 

150 

1.4 

6.5 

82.1 

4.  A 

5.5 

2.7 

O.I 

.1 

O.I 

5-2 

17.1 

0.6 

3-9 

8.9 

160 

I.O 

6.3 

76.6 

6.5 

3.0 

O.I 

.2 

0.4 

4-7 

19.4 

7^6 

1.3 

4-1 

1.4 

8.5 

170 

0.6 

5-9 

70.1 

7m 

3-2 

O.I 

.2 

0.9 

4.1 

21.6 

8.0 

2.2 

4.2 

I.O 

7-9 

1  80 

0.3 

5.3 

62.9 

•2 

3-3 

0.2 

.2 

3-5 

23.6 

8.4 

3-4 

4-2 

0.7 

7-2 

7.8 

190 

O.I 

4.* 

55-.I 

3-4 

°-3 

.2 

2-3 

2-9 

25.2 

8.6 

4-8 

4.2 

0.4 

6-5 

200 

0.0 

4.2 

47.2 

7-9 

3-4 

0.5 

.2 

3-2 

2.3 

26.4 

8.6 

6-3 

4.1 

O.2 

5-7 

210 

O.I 

3-5 

39-3 

7-9 

-i  A 

3-4 

0.5 

.1 

4.1 

1.8 

27.3 

8.5 

7.9 

3-9 

O.I 

4-9 

22O 

°«3 

2.7 

31.7 

7-0 

3-4 

0.6 

.1 

5.1 

1.3 

27.8 

8-3 

9-6 

3-7 

O.O 

4-1 

230 

0.5 

2.0 

24.6 

7-1 

A   l 

3-3 

0.8 

.O 

6.2 

0.9 

27.8 

8.0 

I  1.2 

3-4 

O.I 

3-3 

240 

0.7 

1-3 

18.2 

O.4 

5m 

3.1 

0.8 

0.9 

7.2 

0.6 

27.4 

7-6 

12.8 

0.3 

2.4 

250 

I.O 

0.7 

12.7 

.3 

'  -» 

2.9 

.0 

0.8 

8.3 

0-3 

26.7 

H.2 

2.8 

0.6 

1.7 

260 

1.3 

0-3 

8.0 

4-7 
O  f. 

2.7 

.0 

0.7 

9.2 

O.I 

25.5 

6-1 

I5.6 

2-5 

0.9 

1.2 

270 

1.6 

0.3 

4-4 

o.o 

2.4 

.1 

0.6 

IO.I 

o.o 

24.0 

5.8 

16.8 

2.1 

0.7 

2.6 

280 

1.9 

0.7 

1.8 

2.1 

.2 

0.5 

10.8 

O.I 

22.1 

5.1 

17.6 

1.7 

1.7 

0.4 

290 

2.1 

1.6 

0-3 

1.5 

1.8 

.2 

0.4 

11.3 

0.2 

2O.I 

4-3 

18.4 

1.4 

2.2 

O.I 

300 

2.2 

2.8 

O.I 

O.2 

*«5 

.2 

0-3 

11.8 

0.4 

I7.8 

3-6 

18.8 

I.I 

2-7 

0.0 

310 

2.2 

4-3 

0.9 

2.0 

1.2 

.2 

O.2 

I2.O 

0.7 

154 

2.8 

19.0 

0.8 

3-3 

O.I 

320 

2.2 

5-7 

2.9 

3~ 

0.9 

.2 

0.1 

12.  1 

I.I 

13.0 

2.1 

18.8 

0.5 

3.8 

0.3 

33° 

2.1 

6-9 

6.1 

.2 

41 

0.7 

.1 

O.I 

II.9 

1.6 

I0.5 

1-5 

18.4 

4-3 

0.7 

34° 

2.O 

7-7 

10.2 

•  I 

0.4 

.1 

O.O 

I  1.6 

2.1 

8.2 

I.O 

17.7 

O.I 

4.8 

I.I 

35° 

1.9 

7.8 

'5.5 

A  n 

O.2 

.1 

0.0 

II.  I 

2.7 

6.2 

0.6 

16.8 

o.o 

5-2 

1.7 

360 

1.9 

7-3 

21.5 

o.o 

O.I 

.O 

o.o 

I0.5 

3-3 

4.2 

0.2 

15.6 

o.o 

5-5 

2.4 

TABLE  X. 

Terms  of  the  Co-ordinate  £  to  be  Multiplied  in  t. 

Argument   10. 

"         - 

0° 

i 

2 

3 
4 
5 

+  21,10 
19.47 

17-83 
16.18 

14.51 

12.84 

1.63 
1.64 
1.65 

1.67 
1.67 

45° 
46 

47 
48 

49 
50 

-50.37 

5I-63 
52.86 
54.06 

55.25 
56.41 

1.26 

1.23 
1.20 
I.I9 

i.  §6 

90° 

91 
92 

93 
94 
95 

—  82.65 
82.82 
82.97 
83.09 
83.20 
83.28 

0.17 
o.i  5 

O.I  2 
O.II 

0.08 

135° 
I36 

137 
138 

139 
140 

-71.43 
70.82 
70.18 

69.53 
68.87 
68.20 

0.61 
0.64 
o.65 
0.66 
0.67 

1.68 

i.i3 

0.06 

0.68 

6 

+  ii.  16 

*   A~ 

5' 

-57-54 

96 

-83.34 

141 

-67.52 

7 

9-47 

1.&9 

52 

58.66 

1.12 

97 

83.39 

o.oo 

142 

66.82 

0.70 

8 

I'll 

1.70 

53 

59-75 

1.09 

98 

83.41 

O.02 

H3 

66.  i  o 

0.72 

9 

10 

6.07 
4-37 

1.70 
1.70 

54 
55 

60.82 
61.86 

1.07 

I.o4 

99 

IOO 

8341 
83.38 

O.OO 

o.o3 

144 
H5 

65.38 
64.64 

0.72 
0.74 

1.70 

1.  01 

0.04 

0.75 

1  1 

12 

'3 

+   2.67 
+  0.95 
—  0.76 

1.72 
I.7I 

56 

57 

—62.87 
63.86 
64.83 

0.99 
0.97 

101 

102 
103 

-83.34 
83.28 
83.21 

0.06 
0.07 

146 

-63.89 
63.14 
62.38 

0.75 
0.76 

H 
15 

2-47 
4.18 

I.7I 
I.7I 

59 
60 

65.77 
66.68 

0.94 
0.91 

IO4 
I05 

83.11 
82.99 

0.  10 
O.I  2 

149 
150 

61.59 
60.80 

0.79 
0.79 

I.7I 

0.80 

0.14 

0.80 

16. 

-  5.89 

7-59 

1.70 

61 

62 

-67.57 
68.44 

fmv\f 

0.87 

1  06 

107 

—  82.85 
82.70 

o.i  5 

n  .0 

151 
152 

—60.00 
59.18 

0.82 

_    Qn 

18 

9.29 

1.70 

63 

69.28 

0.84 

108 

82.52 

0.  10 

58.36 

O.o2 
n  O1 

'9 

10.99 

1.70 

/  Q 

64 

70.09 

0.81 

109 

82.32 

O.20 

'54 

57-53 

<>.'    i 

n    OS 

20 

12.67 

I.OB 

65 

70.88 

0.79 

I  IO 

82.11 

O.2I 

'55 

56.68 

O.D3 

1.68 

0.76 

0.23 

o.85 

21 

-H-35 

66 

-71.64 

/ 

1  1  1 

-81.88 

156 

-55.83 

«  Qj» 

22 

16.02 

1.67 

67 

72.38 

0.74 

112 

81.63 

0.25 

'57 

54.96 

0.87 

Q 

23 

17.68 

1.66 

68 

73.09 

0.71 

I  13 

81.36 

0.27 

158 

54.09 

O.87 
QQ 

24 

'9-34 

1.66 

69 

73.78 

0.69 

114 

8  1.  08 

0.28 

159 

53-21 

O.OO 

25 

20.98 

1.64 

70 

74-44 

0.66 

115 

80.78 

o.  3o 

1  60 

52.32 

0.&9 

i.63 

0.63 

0.32 

0.90 

26 

—  22.61 

71 

-75.07 

116 

—  80.46 

_    1  / 

161 

-51.42 

27 

24.22 

1.61 

72 

75-68 

0.61 

117 

80.12 

0.34 

_    -j  e 

162 

50.52 

O.9O 

28 

25.82 

27.41 

1.60 
1.59 

73 
74 

76.27 
76.84 

0.59 
0.57 

118 
119 

79-77 
79.41 

O.J5 
o.36 

_  0_ 

163 

164 

49.60 
48.67 

0.92 

O.93 
_    _1 

3° 

28.98 

1.57 

75 

77.38 

o.54 

120 

79.02 

0.09 

165 

47.74 

0.94 

i.55 

Q.5l 

0.40 

O.94 

31 

-30-53 

76 

-77.89 

121 

-78.62 

1  66 

—46.80 

32 

32.07 

i.54 

77 

78.38 

0.49 

122 

78.21 

0.41 

.  -5 

167 

45.85 

o.95 

33 

33.6° 

1.53 

78 

78.85 

0.47 

I23 

77.78 

0.43 

.  r 

168 

44.89 

0.96 

34 

35-n 

i.5i 

79 

79.30 

0.45 

124 

77-33 

0.45 

./ 

169 

43.92 

0.97 

35 

36.60 

1.49 

80 

79-72 

0.42 

I25 

76.87 

0.46 

170 

42.95 

0.97 

1.4*7 

0.40 

0.48 

0.98 

36 

-38.07 

*  •**  i 

81 

—  80.12 

126 

-76.39 

171 

-41.97 

37 

39-52 

.  1.45 

82 

80.49 

0.37 

127 

75.90 

0.49 

jr 

172 

40.99 

0.98 

38 

40.95 

1.43 

83 

80.84 

o.35 

128 

75.39 

O.DI 

'73 

39-99 

1.00 

39 

42.36 

1.41 

84 

81.16 

0.32 

129 

74.87 

O.52 

r  . 

'74 

38.99 

1.  00 

40 

43-75 

1.39 

85 

81.47 

o.3i 

130 

74-33 

0.94 

'75 

37.98 

1.  01 

4' 

-45.12 

i.37 

86 

-81.75 

0.28 

'3' 

-73-77 

o.56 
F  f 

176 

—  36.96 

1.02 

42 

46.47 

i.  i") 

87 

82.01 

0.26 

I32 

73-2i 

0.90 

K.O 

177 

35-94 

1.02 

43 

47.79 

1.32 

88 

82.24 

0.23 

72.63 

0.3  ' 

t 

178 

34.91 

I.o3 

44 

49.09 

i.3o 

89 

82.46 

0.22 

'34 

72.04 

0.99 

179 

33.88 

i.o3 

45 

50.37 

1.28 

90 

82.65 

O.lg 

71.43 

0.61 

1  80 

32.84 

1.04 

[53] 


TABLE  X.  —  CONCLUDED. 
Terms  of  the  Co-ordinate  £  to  be  Multiplied  in  t. 

Argument  10.  —  Concluded. 

1  80° 
181 
182 

183 

184 
185 

-32.84 
31.80 

30.75 
29.69 

28.63 

27.57 

1.04 
i.o5 
1.  06 
1.  06 
1.  06 

225° 
226 
227 
228 
229 
23O 

+  16.94 
18.04 

19-13 
20.23 
21.32 
22.41 

1.  10 

1.09 

1.  10 

1.09 
1.09 

2700 
271 
272 
273 
^74 
275 

+  59-51 
6O.2O 
60.86 
6l.5I 
62.15 
62.77 

0.69 
0.66 
o.65 
0.64 
0.62 

315° 
316 
317 
318 

319 

320 

+  69.21 
68.81 
68.38 
67.92 
67.42 
66.90 

0.40 
0.43 
0.46 
o.5o 

0.52 

1.07 

1.  08 

» 

0.60 

o.56 

1  86 

—  26.50 

I  O7 

231 

+  23-49 

1.  08 

276 

+  63.37 

o.58 

321 

+  66.34 

o.Sg 

187 
188 
189 
190 

23.26 
22.17 

1  *u  / 
1.09 
1.  08 
1.09 

232 
233 
234 
235 

2+57 
25.65 
26.72 
27.78 

1.  08 
1.07 

1.  06 

277 
278 

279 
280 

63-95 
64.51 
65.06 

65-59 

o.56 
o.55 
o.53 

322 
323 
324 
325 

6575 
65-13 

64.48 

63.79 

0.62 
o.65 
0.69 

1.09 

1.  06 

o.5i 

0.72 

191 

—  21.  08 

236 

+  28.84 

_  _y- 

28l 

+  66.10 

326 

+  63.07 

r 

192 

193 
194 

195 

19.98 

18.88 

17.78 
16.67 

1.  10 

1.  10 
1.  10 

I.  II 

237 
238 

239 
240 

29.89 

30.93 
31.96 

33-00 

I.O3 

1.04 

I.Q.3 

i.o4 

282 
283 
284 
285 

66.59 

67.06 
67-51 
67-94 

0.49 
0.47 
o.45 
0.43 

327 
328 

329 

33° 

62.32 

6i.53 

60.72 
59.87 

0.73 
0.79 

0.81 
o.85 

I.  II 

i.o3 

0.41 

0.88 

196 

197 

-15.56 

14.45 

I.  II 

241 
242 

+  34-03 
35-04 

I.OI 

286 

287 

+  68.35 
68.73 

o.38 

rn  1A 

332 

+  58-99 
58.08 

0.91 

198 
199 

I3-34 

12.22 

I.  II 
1.  12 
I.  II 

243 
244 

36.05 
37.05 

I  .OI 

1.  00 
I.OO 

288 
289 

69.09 
69.42 

O.oO 

o.33 

0.32 

333 

334 

57-1-3 
56.16 

0.97 

I.OI 

200 

II.  II 

245 

38.05 

29O 

69-74 

335 

55.15 

1.  12 

0.98 

o.3o 

1.04 

2OI 

-  9-99 

1.  12 

246 

+  39-03 

0.98 

29I 

+  70.04 

O  27 

336 

+  54-11 

1.07 

2O2 

8.87 

247 

40.01 

v*  7 

292 

70.31 

\j.  &  1 

337 

53-04 

/ 

2O3 

7-75 

1.  12 

1.  12 

248 

40.98 

0.97 
0.96 

293 

70.56 

0.25 
O.22 

338 

51-93 

i  .  1  1 

204 

6.63 

249 

41.94 

294 

70-78 

339 

50-79 

i  i  f\ 

205 

5.50 

25O 

42.89 

0.9 

295 

70.98 

O.2O 

340 

49.63 

1  .  1  U 

i.i3 

0.94 

0.17 

I.I9 

206 

-  4.37 

251 

+  4*3.83 

, 

296 

+  71-15 

n  T^i 

34i 

+  48.44 

1.22 

207 

3-24 

1-1 

252 

44.76 

0.9 

297 

71-3° 

U.  1  J 

342 

47.22 

I  2A 

208 

2.1  I 

i.i 

253 

45.69 

•9 

298 

71.42 

343 

45.98 

1  .  4^ 

209 

-  0.99 

1.  1  2 

254 

46.60 

O.QI 

O.QQ 

299 

7L51 

0.09 
O  O7 

344 

44-  7  i 

1.27 

i.3o 

2IO 

+  0.14 

255 

47.50 

30O 

71-58 

345 

43-4i 

i.i3 

0.89 

O.O4 

i.33 

21  I 

+  1.27 

1.  12 

256 

+  48.39 

0.87 

3OI 

+  71.62 

O.O2 

346 

+  42.08 

i.35 

212 
2I3 

2-39 

3-52 

1.  12 

257 
258 

49.26 
50.13 

0.87 

0.86 

3°2 

303 

71-64 
71.62 

O.O2 
O.O4 

347 
348 

40-73 
39.34 

i.3g 
1.41 

214 

4.64 

259 

50.99 

o  8/! 

3°4 

71-58 

O.O7 

349 

37-93 

I  /!3 

215 

5-77 

I.I 

260 

51-83 

\j,Ucl 

305 

71.51 

35° 

36.50 

1  .q*j 

i.i3 

o.83 

O.IO 

1.45 

216 

+  6.90 

I  .  I  2 

26l 

+  52.66 

0.82 

306 

+  71-41 

0.12 

35i 

+  35-05 

I  47 

217 

8.02 

262 

5348 

0.80 

3°7 

71.29 

o.i  5 

352 

'33.58 

l>4/ 

T   /f\ 

218 

9.14 

I  .  I  2 

263 

54.28 

O»Q 

308 

71.14 

353 

32.09 

1.49 

219 

10.26 

1.  1  2 
1.12 

264 

55.06 

'/ 
0.78 

309 

70.95 

0.22 

354 

30.58 

1.54 

220 

11.38 

265 

55.84 

w.  /u 

3IO 

70.73 

355 

29.04 

1.  12 

0.76 

0.24 

i.56 

221 
222 
223 

+  12.50 
13.61 

14.72 

.1.11 
I.  II 

266 
267 
268 

+  56.60 

57-35 
58.08 

0.75 
0.73 

3H 
312 
3U 

+  70-49 
70.22 
69.91 

O.27 

o.3i 
0.34 

356 
357 
358 

+  27.48 
25.91 
24.33 

i.57 

i.58 

224 
225 

15.83 
16.94 

I  .  I  I 

I.  II 

269 

270 

58.80 
59.5I 

O.72 
0.71 

3H 

69-57 
69.21 

0.36 

359 

360 

22.73 

21.10 

i.63 

[54] 


TABLE  XL 

The  Mean  Anomaly. 

Year. 

Mean  Anomaly. 

t 

Months. 

Mean  Motion. 

t 

H. 

M'n  Motion. 

t 

1850 

324^6'  28".83 

-  °-999 

January  .  .  . 

o°   o'    o".oo 

+  o.ooo 

i 

o°  o'  4  1*45 

+  o.ooo 

1851 

65  38  23  .51 

o.ooo 

February.  . 

8  33  59-88 

+  0.085 

2 

Q       I     22  .90 

+  0.000 

18525 

166  46  53  .02 

I.OO2 

March  .... 

16   18   15  .25 

+  0.162 

3 

0       2       4.35 

+  0.000 

1853 

267  38  47  .69 

2.OOI 

April  

24  52   15  .12 

+  0.246 

4 

o     2  45  .81 

+  o.ooo 

I8C4. 

8    3O    4.2  .37 

3.OOI 

May  

33       9    40  .17 

+0.328 

5 

O       3    27  .26 

+  O.OOI 

JT 

i8cc 

"      J          T        'Jl 

IOQ    22    37    O4. 

. 

+   4*.ooo 

June  

j  j      y     i          / 
4.1    4.3    4.O  .04. 

J 

+  0.41  3 

J 

6 

J             1 

048  .71 

+  O.OO  I 

U5  5 
l8>65 

t^y    *  *     j  /    »»«f 

210  3i     6.cc 

5.002 

July.., 

T          \J     T       "     T 

CO       I       C  .OQ 

*           1      J 

+  0.406 

7 

T_                .  i 

O      4    CO  ,l6 

+  O.OO  I 

I857 

J                O5 
311     23        I   .22 

6.001 

Auguft  .... 

j                j       y 

58  35     4.96 

i        TJ 

+  0.580 

/ 
8 

T     J 

0531  .61 

+  O.OO  I 

1858 

52  14  55  .90 

7.001 

September 

67     9     4  .84 

+  0.665 

9 

o     613  .06 

+  O.OO  I 

I859 

153     6  50.57 

+    8.000 

Oftober... 

75  26  29  .88 

+  0.747 

10 

o     6  54.51 

+  0.001 

1  860  5 

254  15  20  .08 

9.002 

November 

84     o  29  .76 

+  0.832 

1  1 

o     7  35  -97 

+  0.001 

1861 

355     7  H.76 

IO.OOI 

December 

92   17  54  .80   +0.914 

12 

o     817  .42 

+  O.OO  I 

1862 

95  59     9  -43 

I  1.  00  1 

'3 

o     8  58  .87 

+  O.OO  2 

1863 

196  51     4  .10 

+  I2.00O 

'4 

o     9  40  .32 

+  O.OO  2 

18645 

297  59  33  -6l 

I3.O02 

15 

0    10    21   .77 

+  O.OO2 

1865 

38  51  28  .29 

I4.0OI 

* 

16 

Oil        3   .22 

+  O.OO  2 

1866 

139  43  22  .96 

15.001 

17 

o  1  1  44  .67 

+  O.OO2 

1867 

240  35  17  .63 

+  16.000 

18 

0    12    26  .12 

+  0.002 

1868^ 
1869 

341  43  47  -M 
82  35  41  .82 

17.002 
18.001 

Days. 

M'n  Anomaly. 

t 

*9 

20 

o  13     7  .58 
o  13  49  .03 

+  0.003 
+  0.003 

1870 

183  27  36  .49 

19.001 

I 

o°i6'  34".83 

+  0.003 

21 

o  14  30  .48 

+  0.003 

1871 

284  19  31  .17 

+  20.000 

2 

o  33     9  .67 

+  0.005 

22 

o   15   n  .93 

+  0.003 

1872.2? 

25  28     o  .67 

2I.OO2 

3 

o  49  44  .50 

+  0.008 

Z3 

o  15  53  -38 

+  0.003 

1873 

126  19  55  .35 

22.001 

4 

i     6  19  .34 

+  0.0  1  I 

24 

o  16  34.83 

+.0.003 

1874 

227  1  1  50  .02 

23,001 

5 

I     22    54.17 

+  o.o  1  4 

1875 

328     3  44.70 

+  24.0OO 

6 

i  39  29  .01 

+  0.016 

18765 

69    12     14  .21 

25.OO2 

7 

i   56     3  .84 

+  o.o  1  9 

1877 

170     4     8  .88 

26.001 

8 

2     12    38  .68 

+  O.O22 

1878 

270  56     3  .55 

27.001 

9 

2    29     13   .51 

+  0.025 

*.*  In  Bissextile  Years,  fub- 

1879 
i88o5 

ii  47  58  .23 
112  56  27  .74 

+  28.0OO 
29.0O2 

10 
ii 

2  45  48  -35 
3     2  23  .18 

+  O.O27 
+  0.030 

*F 

traft  i  from  the  date  during 
the  firft  two  months. 

1881 

213*48  22  .41 

30.001 

12 

3   18  58  .02 

+  0.032 

1882 

314  40  17  .09 

31.001 

13 

3  35  32  -85 

+  0.035 

1883 

55  32  ii  .76 

+  32.OOO 

H 

3  S2     7  -69 

+  0.038 

18845 

156  40  41  .27 

33.002 

15 

4     8  42  .52 

+  0.041 

1885 

257  32  35  -94 

34-001 

16 

4  25   17  .36 

+  0.043 

1886 

358  24  30  .62 

35.001 

I? 

4  41   52  .19 

+  0.046 

1887 

99  16  25  .29 

+  36.000 

18 

4  58  27  .02 

+  0.049 

18885 

200  24  54  .80 

37.OO2 

*9 

5   15     i  .86 

+  0.052 

1889 

301   16  49  .47 

38.001 

20 

5  31   36.69 

+  0.055 

1890 

42     8  44.15 

39.001 

21 

5  48   ii  .53 

+  0.058 

1891 

143     o  38  .82 

+  4O.OOO 

22 

6     4  46  .36 

+  0.o6o 

18925 

244     9     8  .33 

41.002 

23 

6    21     21    .20 

+  0.063 

1893 

345     i     3  -oi 

42.001 

24 

6  37  56  .03 

+  0.066 

1894 

85  52  57  .68 

43.001 

25 

6  54  30.87 

+  0.069 

1895 

1  86  44  52  .35 

+  44.000 

26 

711     5  .70 

+  0.071 

18965 

287  53  21  .86 

45.002 

27 

7  27  40  .54 

+  0.074 

1897 

28  45   16  .54 

46.001 

28 

7  44  15  -37 

+  0.077 

1898 

129  37   ii  .21 

47.001 

29 

8     o  50  .21 

+  O.O80 

1899 

230  29     5  .88 

+  48.000 

30 

8   17  25  .04 

+  0.082 

1900 

331     21       0  .56 

49.00  I 

31 

• 

8  33  59'-88 

+  0.085 

[55] 


TABLE    XL— CONCLUDED. 
The  Mean  Anomaly. 


MOTION. 

MOTION. 

n. 

In  n  Minutes. 

In  n  Seconds. 

w. 

In  n  Minutes. 

In  n  Seconds. 

i 

o°  o'  o".69 

o°  o'  o".oi 

31 

o°  o'  2  1  ".4  1 

o°  o'  o".36 

z 

1.38 

o  .02 

32 

22  .11 

0-37 

3 

2  .07 

o  .03 

33 

22  .80 

0.38 

4 

2  .76 

o  .05 

34 

23  -49 

o-39 

5 

3-45 

o  .06 

35 

24  .18 

o  .40 

6 

4-H 

o  .07 

36 

24.87 

o  .41 

7 

4.84 

o  .08 

37 

25  -56 

0.43 

8 

5  -53 

o  .09 

'   38 

26  .25 

0.44 

9 

6.22 

o  .10 

39 

26  .94 

0.45 

10 

6  .91 

0  .11 

40 

27  -63 

o  .46 

n 

7  .60 

o  .13 

4* 

28  .32 

0.47 

12 

8  .29 

o  .14 

42 

29  .01 

o  .48 

13 

8  .98 

0.15 

43 

29  .70 

0.49 

H 

9.67 

o  .16 

44 

30.40 

0.51 

15 

10  .36 

0.17 

45 

31  .09 

0.52 

16 

n  .05 

o  .18 

46 

31  -78 

0.53 

17 

n  .74 

o  .20 

47 

32  .47 

0.54 

18 

12  .43 

0  .21 

48 

33  -16 

o-55 

19 

13  -'3 

O  .22 

49 

33.85 

o  .56 

20 

13  .82 

o  .23 

50 

34-54 

0.57 

21 

14.51 

o  .24 

51 

35  .23 

0.59 

22 

15   .20 

0.25 

S2 

35  .92 

o  .60 

23 

15.89 

o  .26 

53 

36  .61 

o  .61 

24 

16.58 

o  .28 

54 

37.30 

o  .62 

25 

17  .27 

o  .29 

55 

37  -99 

o  .63 

26 

17  .96 

o  .30 

56 

38  .68 

o  .64 

27 

1  8  .65 

o  .31 

57 

39.38 

0.66 

28 

19-34 

o  .32 

58 

40.07 

o  .67 

29 

20  .03 

0.33 

59 

40.76 

0.68 

30 

2O  .72 

0.34 

60 

41  .45 

o  .69 

[56] 


TABLE  XII. 

Equation  of  the"  Centre. 

Argument:    The  Correfted  MearT  Anomaly,  M.* 

M. 

D.I' 

M. 

D.I' 

M. 

D.I' 

o°   o' 

10 
20 

3° 

40 

5° 

o°   o'    o".oo 
o     5  59  .61 
o  ii  59  .22 
o  17  58  .81 
o  23   58  .38 
o  29  57  .92 

35.961 
35.961 
35.959 
35.957 
35.954 
35.95i 

8°   o' 

IO 
20 

3° 

40 
50 

4°45'  25"-22 
4  51   16  .17 
4  57     6  .77 
5     2  57  .00 
5     8  46  .87 
5  H  36.35 

35.og5 
35.060 
35.023 
34.987 
34.948 
34.911 

1  6°   o' 

10 

20 

30 
40 

50 

9°i7'34"-79 
9  23     i  .32 
9  28  27  .19 

9  33  52  -41 
9  39  16  .96 
9  44  4°  -84 

32.653 
32.587 

32.522 

32.455 
32.388 

32.320 

I       0 
10 

20 

30 

0  35  57  -43 
o  41   56  .89 

o  47  56  .29 
0  53  55  -65 

35.946 
35.940 
35.936 
35.929 

9     o 

IO 

20 
30 

5  20  25  .46 
5  26  14  .17 
5  32     2  .49 
5  37  5°  -4° 

34.871 
34.832 
34-7QI 

17     o 

10 
20 

3° 

9  50    4  .04 
9  55  26.56 
10    o  48  .38 
1069  .52 

32.252 

32.182 
32.H4 
32.044 

40 
50 

o  59  54  .94 
1     5  54-15 

35.921 
35.911 

40 
5° 

5  43  37  -9° 
5  49  24  .99 

34.709 
34.666 

40 

5° 

10  ii   29  .96 
10  16  49  .70 

31.974 
31.903 

2       0 

i   ii   53  .26 

35.9o3 

IO       0 

5  55   ii  -65 

34.623 

18     o 

10  22     8  .73 

3i.832 

10 
2O 

i   17  52  .29 
i  23  5i  -23 

35.894 
35.884 

10 

20 

6    o  57  .88 
6    6  43  .66 

34.578 
34.535 

IO 

20 

10  27  27  .05 
10  32  44  .64 

31.759 

31.687 

30 
40 

i  29  50  .07 
i  35  48  -80 

35.873 
35.861 

30 
40 

6  12  29  .01 
6  1  8   13  .91 

34.490 
34.443 

30 
40 

10  38     i  .51 
10  43   17  .65 

3i.6i4 
3i.54i 

5° 

i  41  47  .41 

35.848 

50 

6  23  58  -34 

34.398 

5° 

10  48  33  .06 

31.467 

3     ° 

i  47  45  -89 

35.835 

II       0 

29  42  .32 

34.35i 

19     o 

i°  53  47  -73 

3i  3  3 

IO 

i  53  44  -24 

35.820 

IO 

6  35  25  -83 

34-3o2 

10 

10  59     i  .66 

3    3 

20 

i  59  42  -44 

35.8o6 

20 

6  41     8  .85 

34.255 

20 

ii     4  14  .83 

3  i.  243 

3° 

40 

5° 

2     5  40  .50 

211     38  .40 
2    17    36  .13 

35.790 
35.773 
35.757 

30 
40 

5° 

6  46  51  .40 

6  52  33  -46 
6  58   15  .01 

34.206 
34.155 
34.106 

3° 

40 
50 

ii     9  27  .26 
ii   14  38  .93 
ii   19  49  .84 

31.167 
31.091 
3i.oi4 

4     ° 

10 

20 

30 

2  23  33  .70 
22931  .09 
2  35  28  .29 

2    41     25   .30 

35.739 
35.720 
35.701 
35.68i 

12       O 
10 
20 
30 

7     3  56  .07 
7    9  36  .61 
715   1  6  .64 
7  20  56  .15 

34.o54 
34.oo3 
33.95i 
33.8oq 

2O       0 
10 

20 
3° 

ii  24  59  .98 

ii  30    9  -35 
ii  35  37  -93 
1  1  40  25  .74 

30.937 
3o.858 
30.781 

40 

2    47    22   .11 

35.66i 

40 

7  26  35  .14 

V" 

33.845 

40 

ii  45  32  -77 

3o.623 

50 

2  53   18  .72 

35.639 

5° 

7  32  i3  -59 

33.791 

5° 

ii  50  39  .00 

3o.544 

r      o 
IO 

2  59  15  .11 
3     3  ii  .28 

35.617 
35.594 

13     o 

10 

7  37  5i  -5° 
7  43  28  .87 

33.737 
33.68i 

21       0 
10 

ii  55  44-44 
12     o     9  .08 

3o.464 
3o.384 

20 

3  13     7  -22 

35.57o 

20 

7  49     5  -68 

33.626 

2O 

12    5  52  .92 

3o.3o3 

3° 

40 

3  17     2  .92- 

3    22     58   .38 

35.546 
35.521 

30 
40 

7  54  4i  -94 
8     o  17  .63 

33.569 
33.5i2 

3° 
40 

12  10  55  .95 

12    15     58  .l6 

30.221 

3o.i42 

50 

3  2g  53  -59 

35.495 

5° 

8     5   52  -75 

33.454 

5° 

12  20  59  .58 

6     o 

3  34  48  -54 

35.468 

14     o 

8  ii    27  .29 

33.396 

22       o 

12    26       0  .17 

20.076 

IO 
20 

3° 

3  4°  43  -22 
3  46  37  -63 
3  52  3i  -76 

35.441 
35.4i3 
35.385 

10 

20 
30 

8  17      i  .25 
8  22  34  .62 
8  28     7  .40 

33.337 
33.278 
33.2i8 

10 
20 
30 

12  3°  59  -93 
12  35  58  .86 

12    40    56  .96 

77  / 
29.893 
29.8lO 
20.728 

40 

3  58  25  .61 

35.355 

40 

8  33   39.58 

33.i58 

40 

12  45  54.24 

7      / 
29.641 

50 

4    4  19  .16 

35.325 

50 

8  39  ii  .16 

33.097 

5° 

12    50    50  .65 

29.  558 

7     o 

4  10  12  .41 

35.294 

15     ° 

8  44  42  -13 

33.o35 

23     o 

12  55  46.23 

20  473              I 

10 

4  16     5  -35 

35.263 

IO 

8  50  12  .48 

32.973 

10 

13     o  40  .96 

"V"H  fv 

29-388 

20 

4  2i   57  -98 

35.23i 

20 

8  55  42  .21 

32.910 

20 

13   554-84 

2g.3o3 

3° 

4  27  5°  -29 

35.198 

3° 

9     i    ii  -31 

32.847 

30 

13  10  27  .87 

29.216 

40 

4  33  42  -27 

35.i65 

40 

9    6  .39  -78 

32.783 

40 

13    15    20  .03 

5° 

4  39  33  -92 

35.i3o 

5° 

9127  .61 

32.718 

5° 

13    20    1  I    .33 

29.044 

8     o 

4  45  25  -22 

16     o 

9  17  34-79 

24     o 

T3  25     i  -77 

*If  M.  is  >i8o°,  take  360  —  M  as  Argument,  and  the  fign  of  the  Equation  of  the  Centre  negative. 

[571 


TABLE  XII.  —  CONTINUED. 

Equation  of  the  Centre. 

M. 
24°  o' 

10 

i3025'    1*77 
13  29  51  -33 

D.I' 

28.956 
28.869 

M. 

32°  o' 

10 

17     3  25  .28 

D.I' 

24.427 
24.327 

M. 
40°  o' 

10 

i9°55'33"-i9 

19    58    48   .02 

D.I' 

19.482 
19.379 

20 

13  34  40  .02 

28.781 

20 

17     7  28  .55 

24.226 

20 

20       2       I    .8l 

19.274 

30 

13  39  27  .83 

28.693 

3° 

17   ii  30  .81 

24.126 

30 

20    5  14.55 

19.169 

40 

13  44  14.76 

28.695 

4° 

17   15  32  .07 

24.025 

40 

20     8  26  .24 

19.065 

50 

13  49    o  .81 

28.5i6 

50 

17   19  32  .32 

23.925 

50 

20    II    36  .89 

18.960 

25     o 

13  53  45  -97 

28.427 

33     o 

17  23  31  .57 

23.823 

41     o 

20  14  46  .49 

18.855 

10 
20 

13  58  30  .24 
14     3  13  .61 

28.337 
28.247 

10 
20 

17  27  29  .80 
17  31  27  .03 

23.723 
23.621 

10 

20 

20  17  55  -°4 

20    21       2  .54 

18.750 

18.645 

30 

14    7  56  .08 

28.i58 

30 

17  35  23  .24 

23.520 

3° 

20  24     8  .99 

18.540 

40 

14  12  37  .66 

28.067 

40 

17  39  18  .44 

23.418 

40 

20    27    14  .39 

18.436 

5° 

H  17  l8  -33 

27.976 

5° 

17  43  12  .62 

23.3i7 

50 

20  30  18  .75 

i8.33o 

26     o 

14    21    58  .09 

27.885 

34     o 

'7  47     5  -79 

23.215 

42     o 

20    33    22  .05 

18.226 

10 

14    26    36  .94 

27.793 

10 

»7  5°  57  -94 

23.112 

10 

20   36    24  .31 

18.120 

20 

14    31     14.87 

27.702 

20 

17  54  49  .06 

23.011 

20 

20  39  25  .51 

18.016 

30 
40 

50 

14  35  51  .89 
14  40  27  .99 
1-4  45     3  .16 

27.610 
27.517 
27.425 

3° 

40 
50 

17  58  39  .17 
18     2  28  .26 
18     6  16  .32 

22.909 
22.806 
22.704 

30 
40 

5° 

20   42    25   .67 

20  45  24  .78 

2O   48    22  .84 

17.911 
17.806 
17.701 

27     o 

H  49  37  -41 

27.332 

35     o 

18   10     3  .36 

22.601 

43     o 

20    51     19  .85 

17.596 

10 

14  54  10  .73 

27.239 

10 

18   13  49  .37 

22.498 

10 

20  54  15  .81 

17.492 

20 

14  58  43  .12 

27.145 

20 

18   '7  34-35 

22.3g6 

20 

20  57  10  .73 

17.387 

30 

15     3  H-57 

27.052 

3° 

1  8  21    1  8  .31 

22.293 

3° 

21     o    4  .60 

17.282 

40 

5° 

15     7  45  .09 

15     12    24  .67 

26.958 
26.863 

40 
50 

18  25     i  .24 
18  28  43  .13 

22.189 
22.087 

40 

5° 

21     2  57  .42 
21     5  49  .20 

17.178 

17.073 

28     o 

10 

15  16  43  .30 

15    21     IO  .98 

26.768 
26.674 

36     o 

10 

1  8  32  24  .00 
18  36     3  .83 

2i.983 
21.880 

44    o 

10 

21     8  39  -93 

21     II    29  .6l 

16.968 
16.864 

20 

15  25  37  .72 

26.578 

20 

i  8  39  42  .63 

21.776 

20 

21     H      8  -25 

16.759 

30 

15  3°    3  -5° 

26.483 

3° 

1  8  43  20.39 

21.673 

3° 

21   17     5  -84 

16.655 

40 

15  34  z8  -33 

26.387 

40 

1  8  46  57.12 

21.569 

40 

21   19  52  .39 

1  6.55o 

50 

15    38    52  .20 

26.292 

50 

18  50  32  .81 

21.466 

50 

21     22    37   .89 

16.446 

29     o 

15  43  15  .12 

26.195 

37     o 

18  54    7  .47 

21.362 

45     o 

21    25    22   .35 

16.341 

10 
20 

15  47  37  -07 
15  51  58  .06 

26.099 
26.oo3 

10 
20 

1  8  57  41  .09 
19     i   13  .67 

21.258 

2i.i54 

IO 
20 

21  28     5  .76 

21     30   48   .13 

16.237 
i6.i33 

30 
40 

15  56  1  8  .09 
16    o  37  .15 

25.906 
25.809 

30 
40 

19     4  45  .21 

19     8  15  .71 

2i.o5o 
20.946 

30 
40 

21  33  29  .46 

21  36    9  -75 

16.029 
15.925 

50 

16    4  55  .24 

25.71  1 

5° 

19  ii  45  .17 

20.842 

5° 

21  38  49  .00 

i5.82o 

30     o 

IO 

16    9  12  .35 
i  6  13  28  .49 

25.6i4 

38     o 

10 

19  '5  i3  -59 
19   1  8  40  .97 

20.738 
2o.634 

46     o 

10 

21    41    27  .20 

21  44    4-36 

15.716 
i5.6i2 

20 
30 
40 

16  17  43  .64 
16  21  57  .82 

l6    26    II    .02 

25.4i8 

25.320 
25.221 

20 

3° 

40 

19    22       7  .31 

19  25  32  .60 
19  28  56  .84 

20.529 
20.424 

2O.32O 

20 

3° 
40 

21    46   40  .48 

21  49  15  .56 
21  51  49  .60 

i5.5o8 
i5.4o4 
i5.3oi 

5° 

16  30  23  .23 

25.123 

50 

19  32  20  .04 

2Q.2I6 

5° 

21    54    22  .6l 

15.196 

31     o 

16  34  34.46 

25.O24 

39     ° 

19  35  42  .20 

20.112 

47     o 

21     56    54.57 

15.093 

10 

1  6  38  44  .70 

24.924 

10 

19  39     3  -32 

2O.OO7 

10 

21  59  25  .50 

14.989 

20 

16  42  53  .94 

24.826 

20 

19  42  23  .39 

19.902 

20 

22     i  55  .39 

14.887 

30 
40 

50 

16  47     2  .20 
16  51     9  .47 
16  55  15  .74 

24.727 
24.627 

24.527 

3° 

40 
50 

19  45  42  .41 
19  49    o  .38 
19  52  17  .31 

19.797 
19.693 

19.588 

3° 

40 

5° 

22      4    24  .26 
22      6    52  .08 

22    9  18  .87 

s 

14.782 

14.679 
14.575 

32     o 

16  59  21  .01 

40     o 

19  55  33  -19 

_,.       o     22  1  1  44  .02 

[58] 


TABLE  XII.—  CONTINUED. 

Equation  of  the  Centre. 

M. 

D.  i' 

M. 

D.  i' 

M. 

D.  i' 

48°  o' 

IO 

20 
3° 

22°Il'44".62 
22    14      9  .35 

22  16  33  .04 

22  18  55  .70 

14-473 
14.369 
14.266 

14.163 

56°  o' 

IO 

20 
3° 

ti°  A  8'  -7  A"  T-I 

23  4       4  •// 

23  50     i  .17 

23  5i   36  -59 
23  53   ii  .04 

9.640 
9.542 
9.446  ' 
9.348 

64°  o' 

10 
20 

3° 

24  48  30  .27 

24  49  20  .76 
24  50  10  .36 

5.i38 
5.o49 
.4.960 
4.871 

40 
5° 
49     o 

IO 

22   21     17   .33 

22  23  37  .92 
22  25  57  .49 

22   28     l6  .02 

14.069 
13.967 
13.853 

40 

5° 

57     o 

10 

23  54  44  -52 

23   56    17  .02 

23  57  48  .56 
23  59  19  .12 

9.260 
9.  1  54 

9.066 
8.960 

40 
50 
65     o 

10 

24  50  59  .07 
24  51  46  .88 

24  52  33  -8i 
2453   19.85 

4.781 
4.693 
4.604 
4.5i5 

20 

22  30  33  .53 

1  3.  649 

20 

24    o  48  .72 

8.864 

20 

24  54     5  .00 

4.427 

30 
40 

50 

22   32    50  .02 

22  35     5  -49 
22  37  J9  -94 

i3.547 
i3.445 
1  3.  343 

3° 
40 

5° 

24      2     17  .36 

24     3  45  .04 
24    5   ii  .75 

8.768 
•8.671 
8.676 

3° 
40 

50 

24  54  49  .27 
24  55  32  .66 
24  56  15  .18 

4.339 
4.262 
4.164 

50     o 

10 

22  39  33  -37 
22  41  45  -77 

i3.24o 

58     o 

10 

24    6  37  -51 
24    8     2  .30 

8.479 
8.384 

66     o 

10 

24  56  56  .82 

24  57  37  -58 

4.076 

^  nRn 

20 

22  43  57  -H 

i3.o36 

20 

24    9  26  .14 

8.288 

20 

24  58  17  .47 

J.9O9 
3.901 

3° 
40 

22  46       7   .50 
22  48     l6  .84 

12.934 

12.832 

3° 

40 

24  10  49  .02 
24  12   10  .95 

8.193 
8.097 

30 
40 

24  58  56  .48 
24  59  34  .62 

3.8i4 

3.727 

5° 

22   50    25   ,l6 

5° 

24  13   31  .92 

8.oo3 

50 

25    on  .89 

3f  . 

12.731 

.641 

51     o 

IO 

22   52    32   .47 

22  54  38  .76 

12.629 

12  527 

59     o 

10 

24  H  51  -95 
24  1  6  n  .03 

7.908 
7.8i3 

67     o 

10 

25    o  48  .30 
25     i   23  .84 

3.554 

3.468 

20 

22  56  44  .03 

12.426 

20 

24  17  29  .16 

7.718 

20 

25     i   58.52 

3.382 

3° 

22   58    48  .29 

12.325 

30 

24  1  8  46  .34 

7.624 

30 

25    2  32  -34 

3.296 

40 

23    o  51  -54 

12.224 

40 

24  2O       2   .58 

7.53o 

40 

25    3     5  -3° 

3.210 

5° 

23    2  53  .78 

12.123 

5° 

24  21    17  .88 

7-435 

50 

25    3  37  -40 

3.125 

52     o 

23    4  55  -OI 

12.022 

60     o 

24   22     32   .23 

7-341 

68     o 

25    4     8  .65 

3.o3g 

10 

23    6  55  .23 

11.921 

10 

24  23  45  -64 

7.248 

10 

25    4  39  .04 

2.064 

20 

23    8  54.44 

1  1  .820 

20 

24  24    58  .12 

7.164 

20 

25    5     8.58 

*.y*yi* 
2.869 

3° 

23  10  52  .64 

II.72O 

3° 

24  26    9  .66 

7.061 

•  30 

25    5  37  -27 

2.784 

40 

23  12  49  .84 

II.62O 

40 

24  27  20  .27 

6.967 

40 

25    6     5  .11 

2.700 

5° 

23  14  46  .04 

I  l.Slg 

5° 

24  28  29  .94 

6.876 

5° 

25    6  32  .11 

/ 
2.6i5 

53     o 

23  16  41  .23 

11.419 

61     o 

24  29  38  .69 

6.782 

69     o 

25    6  58  .27 

2.53i 

10 

23  18  35  .42 

1I.32O 

10 

24  30  46  .51 

6.689 

IO 

25    7  23  .58 

2.447 

20 

23  20  28  .62 

11.219 

20 

24  3  1   53  -4° 

6.696 

20 

25    7  48  .05 

2.363 

3° 

23   22    20  .8l 

1  1.  1  20 

3° 

2432  59  -36 

6.5o4 

30 

25     8   ii  .68 

2.280 

4° 

23   24    12   .01 

11.020 

40 

24  34    4  -4° 

6.412 

40 

25     8  34.48 

2.196 

50 

23    26       2   .21 

IO.92O 

5° 

2435     8.52 

6.319 

50 

25     8  56  .44 

2.II3 

54    o 

23  27  51  -41 

10.821 

62     o 

24  36  n  .71 

6.228 

70     o 

25    9  17  -57 

2.o3o 

IO 

23  29  39  .62 

10.721 

10 

2437  13  -99 

6.i36  ' 

10   . 

25    9  37  -87 

•  947 

20 

23  31   26  .83 

10.623 

20 

2438  15  -35 

6.044 

20 

25    9  57  -34 

7^  / 
.864 

3° 

23  33   13  .06 

10.524 

30 

24  39  1S  -79 

6.962 

30 

25  10   15  .98 

.782 

40 

23  34  58  -3° 

10.425 

40 

2440  15  .31 

5.862 

40 

25  10  33  .80 

.699 

5° 

23  36  42  .55 

IO.327 

5° 

2441    13  -93 

5.772 

50 

25  I0  5°  -79 

.617 

55     o 

23  38  25  .82 

10.228 

63     o 

24  42   ii  .65 

5.68o 

71     o 

25  1  1     6  .96 

.5'35 

10 

23  40     8  .10 

10.129 

10 

24  43     8  .45 

5.58g 

10 

25    I  I     22  .31 

.453 

20 

23  4i  49  -39 

io.o3i 

20 

24  44     4  -34 

5.499 

20 

25    II     36  .84 

.372 

3° 

23  43   29  .70 

9.933 

3° 

24  44  59  -33 

5.409 

3° 

25    II     50  .56 

.291 

40 

23  45     9  -03 

9-836 

.    40 

24  45   53  .42 

5.3i8 

40 

25    12       3  .47 

200 

50 

23  46  47  -39 

-    _OQ 

50 

24  46  46  .60 

50 

25    12     15  .56 

Q.^OO 

5.229 

.129 

56    'o 

23  48  24  .77 

64    o 

24  47  38  .89 

72     o 

25    12    26  .85 

[59] 


TABLE  XII.—  CONTINUED. 

Equation  of  the  Centre. 

M. 

72°  o' 

25°i2'26".85 

D.I' 

1.047 

M. 
80°  o' 

25°  6'i3'.3o 

D.I' 

2.607 

M. 
88°  o' 

24032'27".58 

D.I' 

5.83o 

IO 
20 

25  12  37  .32 

25    12    46  .99 

0.967 
0.886 

IO 

20 

25    5  47  -23 
25    5  20  .44 

2.679 
2.750 

10 
20 

24  31   29  .28 
24  3°  3°  .36 

5.892 
5.955 

30  |  25  12  55  .85 

0.806 

3° 

25    4  52  .94 

2.822 

30 

24  29  30  .81 

6.018 

40 

25  13     3  -91 

O.727 

40 

25    4  24.72 

2.892 

40 

24  28  30  .63 

6.080 

5° 

25  13   ii  .18 

v"  /  *•  1 
O.646 

5o 

25    3   55  -80 

2.962 

50 

24  27  29  .83 

6.142 

73     o 

25  13  17  .64 

O.567 

81     o 

25    3  26  .18 

3.o33 

89     o 

24  26  28  .41 

6.204 

10 

25  13  23  -31 

w         / 
0.487 

IO 

25    2  55  .85 

3.io4 

10 

2425  26.37 

6.265 

20 

25  13  28  .18 

^        1 

0.408 

20 

25      2    24  .8l 

3.174 

20 

24  24  23  .72 

6.326 

30 
40 

25  13  32  .26 
25  13  35  -55 

0.829 
Q.25O 

3° 
.4° 

25     i  53  .07 

25       I     20  .63 

3.244 
3.3i3 

30 
40 

24  23     20  .46 
24  22     l6  .58 

6.388 
6.449 

5° 

25  13  38  .05 

O.I7I 

50 

25    o  47  .5° 

3.383 

50 

24  21     12  .09 

6.5io 

74    o 

25  13  39  .76 

rf.  »  i 
0.098 

82     o 

25    o  13  .67 

3.453 

90     o 

24  20    6  .99 

6.571 

10 

25  13  40  .69 

0.014 

IO 

t  r\ 

2459  39  -H 

T  A    c  n        i     t~\  *? 

3.522 

10 

*}  rt 

24  19       I   .28 

•7  A     I  n      C  A       Cifl 

6.632 

20 

25  13  40  .83 

0.064 

4*\j 

24  59     3  -92 

3.591 

zu 

Z4  *  7  54  -9° 

6.692 

30 

25  13  40.19 

0.142 

3° 

24  58  28  .01 

3.66o 

30 

24  1  6  48  .04 

6.75i 

40 

25  13  38.77 

0.219 

40 

24  57  5'1  -41 

3.729 

40 

24  15  40  .53 

6.812 

5° 

25  *3  36.58 

0.297 

50 

24  57  14.12 

3.797 

50 

24  H  32  .41 

6.871 

75     o 

25  13  33  .61 

0.374 

83     o 

24  56  36.15 

3.866 

91     o 

24  13  23  .70 

6.932 

IO 

25  13  29.87 

0.452 

IO 

24  55  57  -49 

3.934 

10 

24   12     14  .38 

6.991 

20 

25  »3  25  .35 

0.528 

20 

2455   18.15 

4.00  1 

20 

24  1  1     4  .47 

7.o5i 

3° 

25  13  20  .07 

o.6o5 

3° 

2454  38  .14 

4.069 

30 

24    9  53  -96 

7.109 

40 

25    13     14  .02 

0.682 

40 

24  53  57  .45 

4.i37 

40 

24    8  42  .87 

7.169 

5° 

25  13     7  .20 

0.759 

50 

24  53  1  6  .08 

4.204 

50 

24    7  31  .18 

7.227 

76     o 

25    12    59.6l 

0.835 

84     o 

2452  34.04 

4.272 

92     o 

24    6  1  8  .91 

7.286 

10 

25    12    51    .26 

0.911 

IO 

24  51  51  .32 

4.338 

10 

24    5     6.05 

s 

7.345 

20 

25    12    42  .15 

0.987 

20 

2451     7.94 

4.406 

20 

24    3  52  .60 

7-4o3 

3° 

25    12    32  .28 

.062 

3° 

24  50  23  .88 

4.472 

3° 

24    2  38  .57 

7.461 

40 

25  12  21  .66 

.i37 

40 

2449  39  .16 

4.538 

40 

24    i  23  .96 

7.520 

50 

25    12    IO  .29 

•  •**  / 

.213 

50 

2448  53  78 

4.6o5 

50 

24    o     8  .76 

7.577 

77     o 

25    II     58  .l6 

.288 

85     o 

2448     7-73 

4.671 

93     o 

23  58  52  -99 

7.635 

10 

20 

25  ii  45  .28 
25  ii  31  .65 

.363 
.437 

10 

20 

24  47  21  .02 
2446  33  .65 

4.737 
4.802 

10 

20 

23  57  36  .64 
23  56  19  .72 

7.692 
7.750 

30 

25  ii   17  .28 

.5l2 

30 

2445  45  -63 

4.868 

30 

2355     2.22 

7.807 

40 

25    I  I        2  .16 

.586 

40 

24  44  56  .95 

4.933 

40 

23  53  44  -'5 

7.863 

5° 

25  10  46  .30 

.660 

50 

24  44     7  .62 

4-999 

50 

23  52  25  .52 

7.921 

78     o 

25  10  29  .70 

.735 

86     o 

2443  i7  -63 

5.o64 

94     o 

2351     6.31 

£ 

7-977 

10 

25    10    12  .35 

.808 

10 

24  42  26  .99 

5.129 

10 

23  49  46  -54 

8.o34 

20 

25    9  54.27 

.882 

20 

2441   35  .70 

5.i93 

20 

23  48  26  .20 

8.090 

30 

25    9  35  -45 

.955 

30 

24  40  43  -77 

5.258 

3° 

23  47     5  -30 

8.146 

40 

25    9  '5  -9° 

V 

2.028 

40 

2439  51  -'9 

5.322 

40 

23  45  43  -84 

8.202 

50 

25     8  55  .62 

2.  IOI 

50 

2438  57  -97 

5.386 

50 

23  44  21  .82 

8.258 

79     o 

25     8  34  .61 

2.174 

87     o 

2438     4.11 

5.45o 

95     o 

23  42  59  -24 

8.3i3 

10 

25     8   12  .87 

2.247 

10 

2437     9.6-1 

5.5i4 

IO 

23  41  36  -11 

8.369 

20 

25     7  50.4o 

~-»  / 
2.32O 

20 

2436  14.47 

5.578 

20 

23  40  12  .42 

8.425 

3° 

25     7  27  .20 

2.391 

30 

2435    18  .69 

/ 

5.641 

30 

23  38  48  -17 

8.479 

40 

25     7     3  .29 

2.464 

40 

24  34  22  .28 

5.7o3 

40 

23  37  23  .38 

8.535 

5° 

25     6  38  .65 

2.535 

50 

24  33  25  .25 

v,   i  w 

5.767 

5° 

23  36     8  .03 

8.589 

80     o 

25     6  13  .30 

88     o 

2432  27  .58 

96     o 

23  34  32  .H 

[60] 


TABLE  XII.—  CONTINUED. 

Equation  of  the  Centre. 

M. 

D.I' 

M. 

D.  i' 

M. 

D.  i' 

96°  o' 

IO 

23  33     5  -70 

8.644 
8.698 

104°  o' 

10 

22°I5'36".26 

22  13  45  .47 

11.079 
1  1.126 

112°    0' 
10 

2O    36    22  .15 

13.170 

13.2IO 

20 

23  31   38  .72 

8.753 

20 

22    II     54  .21 

11.174 

20 

20  34  io  .05 

i3.25o 

3° 

40 

23  30  ii  .19 
23  28  33  .12 

8.807 
8.860 

3° 

40 

22    10       2  .47 
22       8     10  .27 

1  1.  2  2O 
11.266 

30 

4° 

20  31   57  .55 
20  29  44  .66 

13.289 
13.329 

50 

'23  27  i4..52 

8.915 

5° 

22       6     17   ,6l 

n.3i3 

5° 

20    27     31    .37 

13.369 

97     o 

23  25  45  .37 

8.968 

105     o 

22       4    24  .48 

11.359 

113     o 

20  25   17  .68 

1  3.4o8 

IO 
20 
30 

23  24  15  .69 

23  22  45  .47 

23    21     14  .72 

9.022 
9.075 
9.128 

10 

20 
30 

22       2    30  .89 
22       O    36  .85 
21    58    42.34 

11.404 
n.45i 
11.496 

IO 
20 
30 

20  23     3  .60 
20  20  49  .13 
20  18  34  .26 

i3.447 
13.487    • 
i3.526 

40 

23  19  43  -44 

9.181 

40 

21  56  47  -38 

11.542 

40 

20  1  6  19  .00 

13.565 

50 

23   1  8   ii  .63 

9-234 

50 

21  54  5i  -96 

11.587 

5° 

20  14     3  -35 

i3.6o3 

98     o 

23   16  39  .29 

9.287 

1  06     o 

21    52    56  .09 

n.633 

114.     o 

20  ii  47  .32 

i3.642 

10 

23  15     6  .42 

9.339 

IO 

21  50  59  .76 

11.678 

-  io 

20     9  30  .90 

i3.68o 

20 

23  13   33  -03 

9.392 

20 

21  49     2  .98 

11.723 

20 

20    7  14  .10 

13.719 

3° 

23  ii   59  -ii 

9-444 

30 

21  47     5  .75 

11.768 

30 

20    4  56  .91 

13.757  . 

40 

23  10  24  .67 

9.496 

40 

21  45     8  .07 

n.8i3 

40 

20     2  39  .34 

13.795 

5° 

23     8  49  .71 

9.548 

5° 

21  43     9  -94 

11.857 

50 

2O       O    21    .39 

13.833 

99     ° 

23     7   14.23 

9.600 

107     o 

21    41     II    .37 

11.902 

115     o 

19  58     3  .06 

13.871 

10 

23     5  38  .23 

9.65i 

IO 

21  39   12.35 

11.946 

10 

19  55  44-35 

13.909 

20 
3° 

23     4     i  -72 
23     2  24  .69 

9.7o3 
9.754 

20 

30 

21  37  12  .89 
21  35   12  .99 

11.990 
I2.o34 

20 

30 

19  53  25  .26 
19  51     5  .80 

13.946 
13.984 

'   4° 
5° 

23     o  47  .15 
22  59     9  .10 

9-8o5 
9.856 

40 
50 

21  33   12  .65 
2131    II  .87 

12.078 

12.122 

40 
50 

19  48  45  .96 
19  46  25  .76 

14.020 
i4-o58 

lop     o 

22  57  3°  -54 

9.907 

108     o 

21    29     IO  .65 

12.166 

116     o 

19  44    5  -18 

14.095 

10 

22  55  51  .47 

9-958 

10 

21  27     8  .99 

12.209 

IO 

19  41  44  .23 

I4.i32 

20 

22    54    II   .89 

10.008 

20 

21  25     6  .90 

12.253 

20 

19  39  22  .91 

14.169 

30 

22    52     31    .8l 

io.o58 

30 

21    23       4.37 

12.295 

30 

19  37     i  .22 

i4-2o5 

40 

22    50    51    .23 

10.109 

40 

21    21        I    .42 

12.338 

40 

19  34  39  -17 

14.242 

50 

22  49  10  .14 

io.  1  58 

5° 

21   1  8  58  .04 

12.382 

50 

19  32  26.75 

14.279 

IOI       0 

22  47  28  .56 

f 

10.209 

109     o 

21  16  54  .22 

12.424 

117     o 

19  29  53  .96 

i4.3i5 

10 

22  45  46  -47 

io.258 

10 

21  14  49  .98 

12.467 

10 

19  27  30  .81 

i4.35i 

20 

22  44     3  .89 

io.3o8 

20 

21  12  45  .31 

12.509 

20 

19  25     7  -3° 

14.387 

30 

22    42    2O  .8l 

10.357 

30 

21     IO    40  .22 

i2.55i 

30 

19  22  43  .43 

14.422 

40 

5° 

22  40  37  .24 
22  38  53  .18 

10.406 
10.455 

40 

5° 

21     8   34.71 

21       6    28  .78 

12.593 
12.636 

40 
50 

19    20    19  .21 

19  17  54  -63 

14-458 
14.494 

IO2       O 

22  37     8  .63 

io.5o4 

IIO       0 

M       4    22  .42 

12.678 

118     o 

19  15  29  .69 

i4-53o 

10 

22  35  23  -59 

10.553 

10 

21        215   .64 

12.719 

10 

19  i-3     4-39 

14.565 

20 

22  33  38  .06 

10.602 

20 

21     o     8  .45 

12.761 

20 

19  io  38  .74 

14.601 

3° 

22    31     52   .04 

io.65o 

30 

20    58       0  .84 

I2.8o3 

30 

19     8  12  .73 

14-635 

40 
50 

22    30       5   .54 
22    28     l8  .55 

10.699 
10.747 

40 
50 

20  55   52  .81 
20  53  44-37 

12.844 
12.885 

40 
50 

19     5  46  .38 
19     3   19  .67 

14.671 

103     o 

IO 
20 

22    26    31    .08 

22  24  43  .13 

22    22     54  .71 

10.795 
10.842 
10.890 

III       O 
10 

20 

20  51   35  .52 
20  49  26  .26 
20  47   1  6  -59 

12.926 
12.967 
i3.oo8 

1  19     o 

10 

20 

19    o  52  .62 

18    58    25   .22 

18  55  57  -47 

14.740 
I4-775 
14.809 

3° 

22    21        5   .8l 

/" 

10.938 

30 

20  45     6  .51 

i3.o48 

3° 

18  53  29  .38 

14.844 

40 

22    19    1  6  .43 

10.985 

40 

20  42  56  .03 

13.089 

40 

1851     o  .94 

14.878 

50 

22    17    26  .58 

II.032 

50 

20  40  45  .14 

13.129 

50 

18  48  32.16 

14.912 

104     o 

22    15     36  .26 

112       0 

20  38  33  -85 

120       0 

1  8  46     3  .04 

[61] 


TABLE   XII.  —  CONTINUED. 

Equation  of  the  Centre. 

M. 

D.  i' 

M. 

D.  i' 

M. 

D.  i' 

120°    O' 

i8°46'  3  '.04 

128°  o' 

I6°40'27*.22 

136°  o' 

i4°23'  56*.7o 

IO 

20 

3° 
40 

50 

'8  43  33  -57 
18  41  3  .77 
18  38  33  -63 
18  36  3  .15 

18  33  32  -34 

14.947 
14.980 

i5.oi4 
i5.o48 
i5.o8i 

10 
20 

3° 

40 

5° 

16  37  42  .83 
16  34  58  .16 
16  32  13  .20 
16  29  27  .97 
1  6  26  42  .45 

16.489 
16.467 
16.496 

16.523 
16.552 

J 

10 

20 
30 
40 

5° 

14  20  59  .97 
14  1  8     3  .02 
14  15     5  .83 
14  12     8  .38 
14    910  .77 

17.673 
17.695 
17.719 
17-745 
17.765 

121       0 

10 

18  31  i  .20 

18  28  29  .72 

i5.i48 

129     o 

10 

16  23  56  .66 
16  21  10  .59 

16.579 
16.607 
it\  M*S 

137     o 

10 

14    612  .90 

14    3   14  .80 

17.787 
17.810 

20 

3° 

40 

5° 

18  25  57  .91 
18  23  25  .77 
18  20  53  .30 
18  18  20  .50 

i5.2i4 
15.247 
1  5.  280 

20 

3° 
40 

5° 

16  18  24  .24 
16  15  37  .62 
16  12  50  .73 
16  10  3  .56 

1  U.UJ  J 

16.662 
16.689 
16.717 

20 

30 
40 

5° 

14    o  1  6  .48 

'3  57   17  -94 
13  54  19  .17 

1351     20  .18 

17.854 
17.877 
17.899 

122       0 
10 
2O 

30 
40 

5° 

18  15  47.38 
18  13  13  .93 
1  8  10  40  .15 
1  8  8  6  .05 
18  5  31  .63 
18  2  56  .89 

i5.3i2 
15.345 
15.378 
i5.4io 
15.442 
15.474 
i5.5o6 

130     o 

10 

20 

30 
40 

5° 

16  7  16  .12 

16  4  28  .41 
1  6  i  40  .43 
15  58  52  .18 
15  56  3  .67 
1553  14  .89 

16.744 
16.771 
16.798 
16.825 

i6.85i 
16.878 
16.904 

138     o 

10 

20 

30 
40 

50 

13   48    20.97 

'3  45  2I  -54 

13   42    21    .89 
13    39    22   .02 
13   36    21    .93 

'3  33  21  .63 

17.921 
17.943 
17.965 
17.987 
18.009 

18.080 
i8.o52 

123     o 

10 

20 

18  o  21  .83 

»7  57  46  -45 
17  55  10  .76 

15.538 
15.569 
i5.6oi 

131     o 

10 
20 

15  50  25  .85 

!5  47  36.54 
1  5  44  46  .97 

16.931 
16.957 
16.988 

139     o 

10 

20 

13    30    21    .11 
13   27    20  .38 
13   24    I9  .43 

18.073 
i8.o95 

30 
40 

5° 

»7  S2  34.75 
17  49  58  .42 
17  47  21  .78 

i5.633 
15.664 
15.695 

30 
40 

5° 

15  41  57  .14 

!5  39  7  -05 
15  36  16  .70 

17.009 
I7.o35 
17.061 

30 

40 

50 

13  21    18  .28 
13  18   16  .92 
'3  15   15  -35 

18.186 
i8.i57 
18.179 

124    o 

17  44  44.83 

15.726 

132     o 

15  33  26  .09 

17.087 

140     o 

13    12     13   .56 

18.200 

10 

1742  7.57 

15.758 

IO 

15  30  35  .22 

17.112 

10 

13    9  ii  .56 

£                                       £ 

18.220 

20 

17  39  29  .99 

15.788 

20 

15  27  44.10 

17.188 

20 

13    6     9.36 

18.241 

30 

17  36  52  .1  1 

15.819 

30 

15  24  52  .72 

17.163 

3° 

13     3     6.95 

18.261 

40 

17  33  13  .92 

i5.85o 

4-0 

15  22  I  .09 

17.188 

40 

'3    o     4-34 

18.281 

50 

17  3i  35  -42 

i5.88i 

50 

15  19  9  .21 

17.214 

5° 

12  57     i  .53 

18.802 

125     o 

10 

20 

17  28  56  .61 
17  26  17  .50 
17  23  38  .09 

15.911 
1  5.941 
15.971 

133     o 

10 

20 

15  1  6  17  .07 
15  13  24  .68 
15  10  32  .04 

17.239 
17.264 
17.289 

141     o 

10 
20 

12  53  58  .51 
12  50  55  .28 
12  47  51  .86 

18.323 

18.842 
18.861 

30 

17  20  58  .38 

16.001 

30 

'5*  7  39  -'5 

/      TT 
17.3l4 

30 

12  44  48  .25 

18.382 

40 

17  18  18  .37 

i6.o32 

40 

15  4  46  .01 

17.338 

40 

12  41  44.43 

18.402 

50 

17  15  38  .05 

16.061 

50 

15  i  52  .63 

17.363 

50 

12   38    40  .41 

18.422 

126     o 

10 

17  12  57  .44 
17  10  16  .53 

16.091 
16.121 

134     o 

10 

14  58  59  .00 
1456  5.12 

17.388 
17.412 

142     o 

10 

12  35  36.19 

12   32     31    .78 

18.441 
18.461 

20 

3° 

17  7  35  -32 
17  4  53  .82 

16.  i5o 
16.179 

20 

30 

1453  ii  .00 
14  50  16  .65 

17.435 
17.460 

20 

3° 

12   29    27  .17 
12   26    22   .37 

18.480 
i8.5oo 

40 
50 

17  212  .03 

1  6  59  29  .94 

16.209 
i6.238 

40 
50 

14  47  22  .05 
14  44  27  .22 

17.483 
17.508 

40 

5° 

12   23     17  .37 
12   20    12  .19 

i8.5i8 
18.538 

127     o 

10 

20 

3° 

16  56  47  .56 
1654  4.89 
16  51  21  .93 

16  48  38  .68 

16.267 
16.296 
16.325 
i6.354 

135     o 

10 

20 

30 

1441  32  .14 

14  38  36  .82 

1435  41  .27 

14  32  45  .48 

17.532 
17.555 
17.579 
17.603 

H3     o 

IO 

20 
30 

12  17     6  .81 

12    14       I    .24 

12  10  55  .48 
12    7  49  -53 

i8.557 
18.576 
18.595 
18.614 

40 

16  45  55  .14 

16.882- 

40 

14  29  49  .45 

17.626 

40 

12    4  43  -39 

18.682 

50 

16  43  ii  .32 

16.410 

50 

14  26  53  .19 

n.64o 

50 

12     i   37.07 

i8.65o 

128     o 

16  40  27  .22 

136     o 

14  23  56  .70 

•  /    ~*+y 

144     o 

ii  58  30.57 

[62] 


TABLE  XII.—  CONTINUED. 

Equation  of  the  Centre. 

M. 

D.I' 

M. 

D.l' 

M. 

D.I' 

144°   o' 

10 

1  1°58'  30^.57 
ii  55   23  .88 

18.669 
18.688 

152°  o' 

10 

9°25'  58"45 
9  22  43  .99 

19.446 
io.45o 

1  60°  o' 

10 

6C48'  2".52 
6  44  42  .36 

20.016 
20.026 

20 
30 
40 

50 

ii  52   1  7  .00 
1  1  49     9  .94 

I  I    46       2  .70 

1  1  42  55  .28 

18.706 
18.724 
18.742 
18.760 

20 
30 

40 
50 

9  19  29  4.0 
91614  .66 

9  I2  59  -79 
9  9  44  .78 

19.474 
19-487 
19.501 

20 

3° 

40 
50 

6  41  22  .10 

6  38  i  .75 

6  34  4i  -3° 
6  31  20  .76 

2o.o35 
2o.o45 
2o.o54 
20  o63 

145     o 

10 
20 

30 
40 

ii  39  47  .68 
ii  36  39  .90 

ii  33  3i  -94 
ii  30  23  .80 
ii  27  15  .49 

18.778 
18.796 
18.814 

i8.83i 
18.848 

153     o 

10 
20 
30 
40 

9  6  29  .63 
9  3  14.35 
8  59  58  -94 
8  56  43  -39 

8  53  27  .71 

19.528 
19.541 
19.555 
19.568 
19.581 

161     o 

10 

20 
30 
40 

6  28  o  .13 
6  24  39  .40 
621  18  .58 
6  17  57  .66 
6  14  36  .66 

20.073 
20.082 
20.092 

20.100 
2O.IIO 

50 

146     o 

1  1  24     7  .01 

II    20    58  .35 

18.866 
18.883 

50 

154    o 

8  50  ii  .90 
8  46  55  .96 

19.594 
10.607 

5° 
162     o 

6  ii  15  .56 

6  7  54.38 

20.118 
20.127 

10 
20 

30 
40 

50 

ii   17  49  .52 
ii   14  40  .52 
ii   ii   31  .34 

II       8    22  .00 
II       512  .48 

18.900 
18.918 
18.934 
i8.g52 
18.969 

10 

20 

30 
40 

5° 

8  43  39  -89 
8  4°  23  .69 
8  37  7  .36 
8  33  5°  -91 
8  3°  34-33 

19.620 
19.633 
19.645 
ig.658 
19.671 

10 

20 

30 
40 

50 

6  4  33  •" 
6  i  ii  .75 

5  57  50  .30 
5  54  28  .76 

5  5i  7  .H 

20.  1  36 
20.145 
20.  1  54 
20.162 
20.170 

147     o 

10 
20 
30 
40 

50 

148     o 

10 

20 

30 
40 

50 

II       22  .79 

10  58  52  .94 
10  55  42  .92 
10  52  32  .73 
10  49  22  .38 
10  46   ii  .87 
10  43     i  .19 

10  39  50.35 
10  36  39  -35 
10  33  28  .19 
10  30  16  .87 

10  27     5  .39 

18.985 
19.002 
19.019 
I9.o35 
ig.oSi 
19.068 
19.084 
19.100 
19.116 
ig.i32 
19.148 
19.163 

155     o 

10 

20 
30 
40 

50 

156     o 

10 

20 

30 
40 

5° 

8  27  17  .62 
8  24  o  .79 
8  20  43  .84 
8  17  26  .76 
8149  .56 
8  10  52  .24 

8  7  34  .80 
8417  .24 
8  o  59  .56 

7  57  4i  -77 
7  54  23  .86 
751  5  .84 

19.683 
19.695 
19.708 
19.720 
19.732 
19.744 
19.756 
19.768 
19.779 
19.791 
19.802 
19.814 

163     o 

10 

20 
30 
40 

5° 
164    o 

10 

20 

3° 
40 

50 

5  47  45  -44 
5  44  23  .65 
5  4i  i  .79 
5  37  39  .84 
5  34  17  .81 
5  30  55  -70 

5  27  33  .5i 
5  24  1  1  .24 

5  20  48  .89 
5  17  26.47 
5  H  3  -97 
5  10  41  -39 

20.179 
20.186 
2o.ig5 

20.203 
20.211 

20.219 
20.227 

20.235 

20.242 

20.250 
20.258 

20.265 

149     o 

10 

20 

3° 
40 

50 

10  23  53  .76 
10  20  41  .97 
10  17  30  .02 
10  14  17  .92 
10  ii     5  .67 
10    7  53  .26 

19.179 
19.195 
19.210 
19.225 
19.241 

157     o 

10 

20 

30 
40 

50 

7  47  47  .70 
7  44  29  .44 
7  41  ii  .07 

7  37  52.59 
7  34  34  .0° 
7  3i  15  -30 

19.826 
19.837 
19.848 
19.859 
19.870 
19.881 

165     o 

10 

20 

30 
40 

50 

5  7  i8.74 
5  3  56  .02 
5  o  33  .23 
4  57  10-36 
4  53  47  42 
4  5°  24  .42 

20.272* 
20.279 
20.287 
20.294 
2o.3oo 
2o.3o8 

150     o 

10 

20 

3° 

40 
50 

151     o 

10 

20 

30 
40 

50 

10    4  40  .70 
10     i   27  .99 

9  58  15  -13 
9  55     2  .12 
9  51  48  .96 
9  48  35  -65 
9  45  22  .20 
9  42     8  .60 
9  38  54-86 
9  35  40  -97 
9  33  26  .94 
9  29  12  .76 

19.271 
19.286 
19.301 
19.316 
ig.33i 
19.345 
19.360 
19.374 
19.389 
19.403 
19.418 
19.431 

158     o 

10 
20 

30 
40 

50 

159     o 

IO 
20 

3° 

40 

5° 

7  27  56  .49 
7  24  37  .57 
7  21  18  .54 

7  17  59  4° 
7  14  40  .16 
7  ii  20  .81 

7  8  i  .36 
7  4  41  .81 
7  i  22  .15 

658  2  .39 

6  54  42  .53 

6  51  22  .58 

19.892 
19.903 
19.914 
19.924 
19.935 
19.945 
19.955 
19.966 
•19.976 
19.986 
19.995 
20.006 

1  66     o 

10 

20 

30 
40 

50 
167     o 

10 
20 
30 

4° 

50 

4  47  i  -34 
4  43  38  .19 
4  40  14  .98 
4  36  51  .70 
4  33  28  .35 
4  30  4  .94 

4  26  41  .47 
4  23  17  .93 

4  19  54-33 
4  16  30  .67 
4  13  6  .95 
4  9  43  -17 

2o.3i5 

20.321 

20.328 
20.335 
20.341 
20.347 
20.354 
2o.36o 
20.366 
20.372 
20.378 
20  384 

152     o 

9  25  58  .45 

1  60     o 

6  48  2  .52 

168     o 

4619  .33 

[63] 


TABLE   XII.  —  CONCLUDED. 

Equation  of  the  Centre. 

M. 

D.I' 

M. 

D.l' 

M. 

D.I' 

168°  o' 

10 

20 

30 
40 

5° 
169     o 

IO 

4°  6'  i9".33 
4  2  55  .43 

3  59  3i  47 
3  56  7  46 
3  52  43  -39 
3  49  19  -26 
3  45  55  -08 
3  42  3°  -85 

20.090 
20.396 
20.401 
20.407 

2o.4i3 
20.418 
20.423 
20.428 

172°  o' 

10 

20    '' 

3° 

40 

5° 
173     o 

10 

2  41     6  .45 
2  37  41  -36 
2  34  l6  -23 

2   30    51    .06 

2  27  25  .86 

2  24      O  .62 

2  20  35  .35 

2o.5o5 
2Q.5og 
2o.5i3 
20.517 

2O.  520 
20.524 

20.527 
2o.53o 

176°  o' 

10 

20 

3° 

40 

50 

177     o 

10 

18  55  -58 
15  29  .82 
12     4  .04 
8  38  .24 
5   12  43 
i     i  46  .60 

0  58    20  .76 

20.575 
20.576 
20.578 
2o.58o 
2o.58i 
20.583 
20.584 
20.585 

20 

30 
40 

5° 
170     o 

10 
20 

3° 
40 

5° 
171     o 

10 
20 

30 
40 

50 

172     o 

339  6.57 
3  35  42  .23 
3  32  17  -84 
3  28  53  .41 

3  25  28  .92 
322  4.38 
3  18  39  .80 

3  15  15  -17 
31150  .49 

3  8  25  .77 

35  *  -oo 
3  i  36  .19 
25811  .34 

2  54  46  44 
2  51^21  .50 

2  47  56  .52 
2  44  31  .51 

20.434 
20.439 
20.443 

2C.449 
20.454 
20.458 
20.463 
20.468 
20.472 

20.477 
20.481 
20.485 
20.490 
20.494 
20.498 

20.501 

20 

30 
40 

50 

174     o 

IO 

20 

30 
40 

50 

175     o 

10 
20 

30 
40 

50 

176     o 

2   17     10  .05 

2   13    44.71 
2   10    19  .34 

2    6  53  .94 

2    3  28  .51 
203  .05 
56  37  .56 

53   12  .05 
49  46  .5  1 

46    20  .94 

42  55  -35 

39  29  -74 
*    36    4  .10 

32  38  44 

29    12  .76 

25  47  .06 

I    22    21   .33 

20.534 

20.540 

20.543 
20.546 
20.549 
2o.55i 
20.554 
20.557 
2o.55g 
2o.56i 
20.564 
2o.566 
20.568 
20.570 
20.573 

20 

30 
40 

50 

178     o 

10 

20 

.          30 
40 

50 

179     o 

IO 

20 

3° 
40 
50 
r  80     o 

o  54  54.91 
o  51   29  .04 
o  48     3.16 
o  44  37  .26 

o  41    ii  .36 

0  37  45  45 
0  34  19-53 
o  30  53  .60 
o  27  27  .66 
o  24     i  .71 

o  20  35  .76 
o  17     9  .81 

o  13  43  -85 
o  10  17  .89 
o    6  51  .93 
o    3  25  .96 

o    o  oo  .00 

20.587 
20.588 
20.590 
20.5go 
20.591 
2o.5g2 
20.593 
2o.5g4 
20.595 
2o.5g5 
20.595 
20.596 
20.596 
20.596 
20.597 
20.596 

' 

[64] 


TABLE  XIII. 

Logarithm  of  the  Elliptical  Radius  Vector. 

Argument  :  The  True  Anomaly,  v* 

t) 

U 

p 

V. 

i* 

V. 

_ 

V. 

^, 

0°  0' 

0.2597938 

o.3 

8°  0' 

0.2605536 

32.  0 

1  6°  o' 

0.2628260 

63.3 

10 

0.2597941 

i  .0 

10 

0.2605856 

32.6 

IO 

0.2628893 

64.0 

20 

0.2597951 

1.6 

20 

0.2606182 

33.3 

20 

0.2629533 

64.6 

3° 

0.2597967 

2.3 

3° 

0.2606515 

33.Q 

30 

0.2630179 

65.2 

40 

0.2597990 

3.0 

40 

0.2606854 

34.6 

40 

0.2630831 

65.9 

50 

0.2598020 

3.6 

50 

0.2607200 

35.2 

5° 

0.2631490 

66.5 

I   O 

0.2598056 

4.3 

9  ° 

0.2607552 

35.0 

17  o 

0.2632155 

AT  o 

10 

0.2598099 

5.Q 

10 

0.2607911 

36.5 

10 

0.2632827 

u  /•* 
67.8 

20 

0.2598149 

5.6 

20 

0.2608276 

•}-,  n 

20 

0.2633505 

68.5 

30 

0.2598205 

6.3 

3° 

0.2608648 

O7.2 
37  0 

3° 

0.2634190 

60.  i 

40 

0.2598268 

6  o 

40 

0.2609027 

o  /.y 

38.5 

40 

0.2634881 

69.8 

5° 

0.2598337 

u.y 
7.6 

50 

0.2609412 

39.2 

50 

0.2635579 

70.4 

2   0 

0.2598413 

8.3 

IO   O 

0.2609804 

3n  S 

18  o 

0.2636283 

/  v>t* 

IT  ¥ 

IO 

0.2598496 

8  Q 

10 

0.2610202 

09.0 
/n  ^ 

10 

0.2636994 

71.1 
1  T  1 

2O 

0.2598585 

u.y 
0.6 

20 

0.2610607 

4*-*.  J 

/i  i 

20 

0.263771  1 

71.7 

T2  3 

30 

0.2598681 

V'v 
IO.2 

30 

o.26nof8 

41  *  1 

4i.8 

30 

0.2638434 

I**" 

73.O 

40 

0.2598783 

IO.O 

40 

0.261  1436 

/o  £ 

40 

0.2639164 

73.6 

5° 

0.2598892 

•w«y 

ii.  5 

50 

0.2611861 

4*2.  J 
43.1 

50 

0.2639900 

74.3 

3  o 

0.2599007 

12.2 

II   0 

0.2612292 

/•}  O 

19  o 

0.2640643 

/***^* 

*f  /  O 

IO 

0.2599129 

12  O 

10 

0.2612730 

40.0 

//  / 

10 

0.2641392 

74-9 
75.6 

20 

0.2599258 

*T*T» 

i3.5 

20 

0.2613174 

44.4 

45.1 

20 

0.2642148 

76.3 

3° 

°-2599393 

14.2 

3° 

0.2613625 

45  7 

30 

0.264291  1 

76.8 

40 

°-2599535 

14.8 

40 

0.2614082 

**'-'•  / 

/.h  A 

40 

0.2643679 

77  5 

5° 

0.2599683 

i5.5 

5° 

0.2614546 

4«J.4 
47.  Q 

50 

0.2644454 

77.  J 
78.1 

4  o 

0.2599838 

16.2 

12   0 

0.2615016 

**  /*u 

X*T  -7 

20  o 

0.2645235 

/   j 
78.8 

10 

0.2600000 

16.8 

10 

0.2615493 

47.7 

/Q  x 

10 

0.2646023 

20 

0.2600168 

17.5 

20 

0.2615977 

40.4 

20 

0.2646817 

79-4 
80.0 

3° 

40 

0.2600343 
0.2600525 

*  F*"* 

18.2 
1  8.8 

30 
40 

0.2616467 
0.2616963 

49*O 

49.6 
5o,3 

3° 
40 

0.2647617 
0.2648424 

80.7 
8i.3 

5° 

0.2600713 

19.5 

50 

0.2617466 

5i.o 

5° 

0.2649237 

82.0 

5  ° 

0.2600908 

2O.I 

13  o 

0.2617976 

'ii  fi 

21   0 

0.2650057 

82.6 

IO 

0.2601  109 

20.8 

IO 

0.2618492 

j  i  *\j 

52  2 

10 

0.2650883 

83.3 

20 

0.2601317 

21.4 

20 

0.2619014 

52  O 

20 

0.265  1716 

83.  9 

3° 

0.2601531 

22.1 

3° 

0.2619543 

53.6 

3° 

0.2652555 

84.5 

40 

0.2601752 

22.7 

40 

0.2620079 

54.2 

40 

0.2653400 

85.2 

50 

0.2601979 

/ 

23.4 

50 

0.2620621 

54.8 

50 

0.2654252 

85.8 

6  o 

0.2602213 

24.1 

14  o 

0.2621  169 

55.5 

22   O 

0.26551  10 

86.4 

10 

0.2602454 

24.7 

10 

0.2621724 

56.2 

10 

0.2655974 

87  i 

20 

0.2602701 

*•-+•  / 
25.4 

20 

0.2622286 

56.8 

2O 

0.2656845 

07.1 

8-T  7 

3° 

0.2602955 

26.O 

3° 

0.2622854 

IT  / 

3° 

0.2657722 

07.7 
QQ  / 

40 

0.2603215 

26.7 

40 

0.2623428 

^7.4 

58.i 

40 

0.2658606 

00.4 
8o.O 

50 

0.2603482 

f.\j.  i 
27.4 

5° 

0.2624009 

58.8 

5° 

0.2659496 

89.6 

7  o 

0.2603756 

28.0 

15  o 

0.2624597 

'in  X 

23  o 

0.2660392 

10 

0.2604036 

28.7 

10 

0.2625191 

^y.iv 
60  I 

10 

0.2661295 

90.  \J 

20 

0.2604323 

BVl  / 

29.3 

20 

0.2625792 

20 

0.2662204 

90.9 

3° 

0.2604616 

3o.o 

30 

0.2626399 

6l,4 

30 

0.2663119 

9I«5 

40 

0.2604916 

3o.i 

40 

0.2627013 

62.0 

40 

0.2664041 

92.2 

r»O  ft 

5° 

0.2605223 

'  •  / 
3i.3 

50 

0.2627633 

62  i 

50 

0.2664969 

y  .£.0 
r*3  / 

8  o   0.2605536 

16  o 

0.2628260 

\j&.  I 

24  o 

0.2665903 

9^*4 

*  If  v.  is  >  1  80°,  take  1  80  —  v.  as  the  Argument. 

[651 


* 

TABLE  XIII.—  CONTINUED. 

Logarithm  of  the  Elliptical  Radius  Vector. 

V. 

24°  o' 

0.2665903 

p 

V. 

32°  o' 

0.2718109 

? 

V. 

40°  o' 

0.2784370 

p 

IO 

0.2666843 

94.0 

10 

0.2719348 

"* 

10 

0.2785895 

rQ     - 

20 

0.2666790 

94.7 

20 

0.2720593 

1  24-5 

20 

0.2787427 

IOO.  3 

30 
40 

0.2668743 
0.2669702 

95.9 

rvA   A 

30 
40 

0.2721844 
0.2723102 

I  2  J.  I 

125.8 
126.3 

3° 
40 

0.2788964 

0.2790507 

i53.7 
1  54.  3 

50 

0.2670668 

90.0 

50 

0.2724365 

5° 

0.2792056 

154.9 

25     o 

0.2671640 

97.2 

__    Q 

33     o 

0.2725635 

127.0 

41     o 

0.2793610 

i55.4 

r  r 

IO 

0.2672618 

97.0 

rtft  t\ 

10 

0.2726910 

1  27.5 
128.2 

10 

0.2795170 

I  JO.O 
llA   A 

20 

0.2673603 

QO,  J 

20 

0.2728192 

t  08  8 

20 

0.2796736 

1  JO.O 

30 

0.2674594 

99.1 

30 

0.2729480 

I  2O.  o 

3° 

0.2798307 

157.1 

40 
50 

0.2675591 

0.2676595 

99-7 
100.4 

101  .0 

40 
5° 

0.2730774 
0.2732074 

129.4 

i3o.o 
i3o.6 

40 
5° 

0.2799884 
0.2801467 

157.7 
i58.3 
1  58.  9 

26     o 

10 

0.2677605 
0.2678621 

ioi.  6 

IO2.3 

34    o 

10 

0.2733380 
0.2734692 

l3l.2 

i3i.8 

42     o 

10 

0.2803056 
0.2804650 

1  5g.  4 

20 

0.2679644 

102.9 

20 

0.2736010 

i32.4 

20 

0.2806251 

160.  i 
160.6 

30 

0.2680673 

io3.5 

3° 

•0.2737334 

i33.i 

3° 

0.2807857 

40 

0.2681708 

104.1 

40 

0.2738665 

i33.6 

40 

0.2809469 

lol  .  2 

5° 

0.2682749 

104.8 

5° 

0.2740001 

5° 

0.281  1086 

101.7 

162.3 

27     o 

0.2683797 

io5.4 

35     o 

0.2741343 

i34.8 

43     o 

0.2812709 

10 

0.2684851 

106.0 

10 

0.2742691 

i35.4 

10 

0.2814338 

I  O2  .9 

i63.4 

20 

0.268591  1 

1  06.  6 

20 

0.2744045 

i36.o 

20 

0.2815972 

164  o 

30 
40 

0.2686977 
0.2688049 

107.2 

IO7.O 

30 
40 

0.2745405 
0.2746771 

136.6 
137.2 

30 
40 

0.2815612 
0.2819258 

164.6 

i65.i 

50 

0.2689128 

/•y 
1  08.  5 

50 

0.2748143 

137.8 

5° 

0.2820909 

165.7 

28     o 

0.2690213 

109.1 

36     o 

0.2749521 

i38.4 

44     o 

0.2822566 

166.2 

10 
20 

30 

0.2691304 
0.2692401 
0.2693505 

109.7 
110.4 

1  1  1.O 

20 
30 

0.2750905 
0.2752295 
0.2753691 

i3g.o 
139.6 

lAO.  2 

IO 

20 
3° 

0.2824228 
0.2825897 

0.2827571 

166.9 
167.4 

40 

0.2694615 

1  1  1  .6 

40 

0.2755093 

I4O.8 

40 

0.2829250 

167.9 

5° 

0.2695731 

112.2 

5° 

0.2756501 

I4I.4 

5° 

0.2830935 

1  60.  i 

29     o 

10 

0.2696853 
0.2697982 

II2.9 

n3.5 

37     o 

10 

0.2757915 
0.2759334 

I4I.9 

142.6 

45     o 

IO 

0.2832626 
0.2834322 

V    * 

169.6 

20 

0.2699117 

1  14.  1 

20 

0.2760760 

143.2 

20 

0.2836024 

1  70.  2 

30 

0.2700258 

1  14.7 

30 

0.2762192 

3° 

0.2837731 

170.7 
171.3 

40 

0.2701405 

ii5.3 

40 

0.2763629 

1  44.  3 

40 

0.2839444 

5° 

0.2702558 

116.0 

5° 

0.2765072 

144.9 

5° 

0.2841  163 

171.9 
172.4 

30     o 

0.2703718 

116.6 

38     o 

0.2766521 

145.5 

46     o 

0.2842887 

10 

0.2704884 

i  n  2 

IO 

0.2767976 

146.1 

10 

0.2844617 

173.5 

20 

0.2706056 

1  1  /.  f. 
117.7 

20 

0.2769437 

146.7 

20 

0.2846352 

I74.I 

3° 

0.2707233 

118.4 

3° 

0.2770904 

147.3 

3° 

0.2848093 

174.6 

40 

0.2708417 

I  IQ.Q 

40 

0.2772377 

T  XT  o 

40 

0.2849839 

175  2 

50 

0.2709607 

II9.6 

50 

0.2773856 

14  /.y 
148.4 

5° 

0.2851591 

175.7 

31     o 

0.2710803 

I  20.  2 

39     o 

0.277534° 

I49-O 

47     o 

0.2853348 

I  76.  2 

10 

20 

0.2712005 

0.2713214 

120.9 
I2I.4 

10 

20 

0.2776830 
0.2778327 

149-7 

1  5o.  2 

10 
20 

0.28551  10 

0.2856878 

176.8 

30 

0.2714428 

I  22.  1 

30 

0.2779829 

i5o.8 

30 

0.2858652 

l  "n  n 

40 

0.2715649 

122.7 

40 

0.2781337 

1  5l  .A 

40 

0.286043  l 

1  /  rv 
Tl8  A 

5° 

0.2716876 

123.3 

5° 

0.2782851 

5° 

0.2862215 

1  70.4 
179.0 

32     o 

0.2718109 

40     o 

0.2784370 

48     o 

0.2864005 

[66] 


TABLE  XIII.—  CONTINUED. 

Logarithm  of  the  Elliptical  Radius  Vector. 

V. 

48°   o' 

IO 

20 

30 
40 

0.2864005 
0.2865801 
0.2867602 
0.2869409 
0.2871220 

0 

179.6 
180.1 
180.7 
181.1 
181.7 

V. 

56°  o' 

10 

20 

30 
40 

0.2956146 
0.2958191 
0.2960242 
0.2962297 
0.2964357 

204.5 

205.1 

ao5.5 
206.0 
206.5 

64°  o' 

IO 

20 

30 
40 

0.3059716 
0.3061986 
0.3064261 
0.3066540 
0.3068823 

227.0 
227.5 
227.9 
228.3 
228.8 

50 

0.2873037 

i8a.3 

50 

0.2966422 

207.0 

50 

0.3071111 

229.2 

49     ° 

10 

0.2874860 

0.2876688 

182.8 
i83.3 

57     o 

IO 

0.2968492 
0.2970567 

207.5 

65     o 

10 

0.3073403 

0.3075699 

229.6 

23o.i 

20 

0.2878521 

i83.8 

20 

0.2972647 

2Qo.O 
208.4 

20 

0.3078000 

23o.5 

30 
40 

50 

0.2880359 
0.2882203 
0.2884052 

184.4 
184.9 
i85.5 

30 
40 

50 

0.2974731 
0.2976821 
0.2978915 

209.0 
209.4 

30 
40 
50 

0.3080306 
0.3082615 
0.3084929 

23o.g 
23i.4 

a3i.8     ' 

50     o 

0.2885907 

186.0 

58     o 

0.2981014 

*2\Q     A 

66     o 

0.3087247 

232.2 

IO 

0.2887767 

186.6 

IO 

0.2983118 

10 

0.3089569 

232.6 

20 

3° 

0.2889633 
0.2891503 

187.0 
187.6 

20 
30 

0.2985227 
0.2987340 

2  10.9 
211.  3 

20 

30 

0.3091895 

0.3094226 

233.1 
233.5 

40 

0.2893379 

188.1 

40 

0.2989459 

2II-9 

40 

0.3096561 

233.9 

5o 

0.2895260 

188.7 

50 

0.2991582 

2  1  2.O 
212.8 

5° 

0.3098900 

234.3 

51     o 

0.2897147 

189.1 

59     o 

0.2993710 

2i3.3 

67     o 

0.3101243 

234.7- 

10 

0.2899038 

189.7 

IO 

0.2995843 

2i3.8 

IO 

0.3104590 

mv^»  I 

235.1 

20 

0.2900935 

1QO.  2 

20 

0.2997981 

20 

0.3105941 

235.6 

3° 
40 

0.2902837 
0.2904745 

IQO.S 
IQ  I    2 

3° 

40 

0.3000123 
0.3002270 

2  14*  2 

214.7 

3° 

40 

0.3108297 
0.3110657 

236.o 
236.4 

50 

0.2906657 

191.8 

50 

0.3004422 

2  1  0.  2 

50 

0.3113021 

236.8 

52     o 

0.2908575 

*  7 

60     o 

0.3006579 

68     o 

0.3115389 

237.  2 

10 

0.2910499 

IQ2.8 

IO 

0.3008740 

2  IO.  I 

216.6 

10 

0.31  17761 

237.6 

20 

0.2912427 

*  V       ^ 
193.3 

20 

0.3010906 

20 

0.3120137 

238.o 

30 

0.2914360 

In'}  n 

30 

0.3013077 

217.1 

3° 

0.3122517 

238.4 

40 

0.2916299 

190.9 
194.4 

40 

0.3015252 

217.3 

2  17.  Q 

40 

0.3124901 

238.8 

5° 

^0.2918243 

194.9 

50 

0.3017431 

218.5 

5° 

0.3127289 

239.2 

53     o 

0.2920192 

m*)  /. 

61     o 

0.3019616 

218.0 

69     o 

0.3129681 

10 

0.2922146 

1  y-'*4 
195.9 

10 

0.3021805 

219.4 

10 

0.3132077 

24Q.O 

20 

3° 

0.2924105 
0.2926069 

196.4 

JQ7  O 

20 
30 

0.3023999 
0.3026197 

219.8 

220.3 

20 

30 

0.3  '34477 
0.3136881 

240.4 
24O.8 

40 

0.2928039 

V  /•" 
197.5 

40 

0.3028400 

22O.8 

40 

0.3139289 

241.2 

50 

0.2930014 

198.0 

5° 

0.3030608 

221.2 

50 

0.3141701 

241.6 

54     o 

0.2931994 

198.5 

62     o 

0.3032820 

221  6 

70     o 

0.3144117 

242.O 

IO 

0.2933979 

IO 

0.3035036 

IO 

o-3'46537 

20 

0.2935969 

I99.O 

20 

0.3037257 

222.1 
222  6 

20 

0.3148961 

242.8 

3° 

0.2937964 

20O.O 

3° 

o-3039483 

223.0 

3° 

0.3151389 

243.1 

4° 

0.2939964 

2OO.5 

40 

0.3041713 

223.4 

40 

0.3153820 

243.5 

5° 

0.2941969 

2OI.O 

5° 

0-3043947* 

224.O 

50 

0.3156255 

243.9 

55     ° 

0.2943979 

201  .6 

63     o 

0.3046187 

71     o 

0.31  58694 

o  /  /   "3 

10 

0.2945995 

2O2  O 

10 

0.3048431 

224.8 

10 

0.3161137 

^44.O 

0  /  /      M 

20 

0.2948015 

202.5 

20 

0.3050679 

225.2 

20 

0.3163584 

^44.7 
245.0 

30 

0.2950040 

2o3.o 

30 

0.3052931 

30 

0.3166034 

245  5 

40 

0.2952070 

2o3.6 

40 

0.3055188 

226.2 

40 

0.3168489 

245.8 

50 

0.2954106 

204.0 

5° 

0.3057450 

226.6 

50 

0.3170947 

246.2 

56     o 

0.2956146 

64     o 

0.3059716 

72     o 

0.3173409 

[67] 


TABLE  XIII.—  CONTINUED. 

Logarithm  of  the  Elliptical  Radius  Vector. 

V. 

72°  o' 

0.3173409 

d 

80°   o' 

0.3295663 

d 

V. 
88°   o' 

0.3424646 

O 

10 
20 

0.3175875 
0.3178344 

246.0 

246.9 
o  /_  o 

1C 
20 

0.3298288 
0.3300916 

2O2.  3 

262.8 

10 

20 

0.342739* 
0.3430*37 

274.5 
274.6 

3° 

0.3180817 

247-0 

30 

0.3303547 

•f 

30 

0.3432884 

274.7 

40 

5° 

0.3183294 
0.3*85774 

247.7 
248.0 

40 
50 

0.3306181 
0.3308818 

263.7 

40 

5° 

0.3435633 
0.3438385 

274.9 
275.2 

248.4 

264.0 

275.4 

73     o 

10 

0.3188258 
0.3190746 

248.8 

81     o 

10 

0.3311458 
0.3314101 

264.3 

89     o 

IO 

0.3441139 

0.3443895 

275.6 

20 

0.3*93237 

249.1 
24Q.5 

20 

0.3316746 

264.9 

20 

0.3446653 

276.0 

30 
.      4° 

0.3195732 
0.3198230 

*"+7 
249.8 

250.2 

30 
40 

0-33*9395 
0.3322046 

265.1 
265.4 

3° 
40 

0-34494*3 
0.3452174 

276.1 
276.3 

5° 

0.3200732 

5° 

0.3324700 

_/  r    f 

5° 

0-3454937 

25o.5 

2OD.O 

276.5 

74    o 

10 

0.3203237 
0.3205746 

250.9 

25l  .2 

82     o 

10 

0.3327356 
0.3330015 

265-9 
266  2 

90     o 

10 

0.3457702 
0.3460469 

276.7 

20 

0.3208258 

20 

0.3332677 

266.4 

20 

0.3463237 

27  - 

30 

0.3210774 

V 

30 

0-333534* 

266  7 

3° 

0.3466007 

277.0 

40 

0.32*3294 

0.3215817 

232.  0 
252.3 

252.6 

40 
50 

0.3338008 
0.3340678 

267.0 
267.2 

40 
50 

0.3468779 
0.347*552 

277.2 
277.3 
277.5 

75     ° 

0.3218343 

83     o 

0-334335° 

A      * 

91     o 

0.3474327 

10 

0.3220873 

*M  1 

10 

0.3346025 

207.3 
267.8 

IO 

0.3477104 

277.7 

20 

0.3223406 

253 

20 

0.3348703 

268.O 

20 

0.3479882 

277.8 
278.0 

30 
40 
50 

0.3225943 

0.3228483 
0.3231026 

254-0 
254.3 
254-7 

3° 

40 
50 

o.3354o66 
0.335675* 

268.3 
268.5 

3° 

40 
50 

0.3482662 
0.3485443 
0.3488226 

278.1 
278.3 
278.5 

76     o 

10 

0.3233573 
0.3236123 

255.  o 

84     o 

10 

0.3359439 
0.3362129 

269.0 
269.3 

92     o 

10 

0.3491011 

0-3493797 

278.6 

20 

30 

0.3238677 
0.3241234 

255.7 
256.O 

20 

30 

0.3364822 
0.3367517 

269.5 
269.7 

20 

3° 

0.3496585 
0-3499374 

278.9 
279.0 

40 
50 

0.3243794 
0.3246358 

256.4 
256.6 

40 
50 

0.3370214 
0.33729*4 

270.0 
270.3 

40 
50 

0.3502164 
0.3504956 

279.2 
279.3 

77     o 

0.3248924 

257.0 

85     o 

0.3375617 

270.5 

93     o 

0.3507749 

279.5' 

10 
20 

30 
40 

0.325*494 
0.3254067 

0.3256644 
0.3259224 

257.3 

257-7 
258.Q 

258.2 

IO 

20 

3° 

40 

0.3378322 
0.3381029 

0.3383738 
0-3386450 

270.7 
270.9 
271.2 
271.4 

IO 

20 

3° 
40 

0.3510544 

0.35*334° 
0.3516137 

0.35*8935 

279.6 
279.7 
279.8 
280.0 

50 

0.3261806 

258.6 

50 

0.3389*64 

*•  /  *  •*» 
271.6 

50 

0.352I735 

280.1 

78     o 

0.3264392 

258.9 

86     o 

0.3391880 

271  O 

94     o 

0.3524536 

280.2 

10 

0.3266981 

259.2 

10 

0-3394599 

/  *  *y 

272.1 

IO 

0.3527338 

280.4 

20 

30 

0.3269573 
0.3272169 

259.6 
259.8 

20 

30 

0.3397320 
0.3400043 

272.3 
272.5 

20 
30 

0.3530142 
0.3532946 

280.4 
280.6 

40 

0.3274767 

*       7     v 

260.  2 

40 

0.3402768 

272.7 

40 

0.3535752 

280.7 

50 

0.3277369 

260.4 

50 

0.3405495 

273.0 

50 

0.3538559 

280.8 

79     o 

10 

0.3279973 

0.3282581 

260.8 

261  o 

87     o 

10 

0.3408224 
0.3410956 

273.2 
273.4 

95     o 

10 

0.354*367 
0.3544*76 

280.9 
281.1 

20 

0.3285191 

261.3 

20 

0.34*369° 

273.6 

20 

0.3546987 

281.2 

30 

0.3287804 

2OI   *7 

3° 

0.3416426 

273.8 

30 

0-3549799 

281.2 

40 

0.3290421 

262.0 

40 

0.3419164 

274.0 

40 

0.355261  1 

281.3 

50 

0.3293041 

262.2 

50 

0.3421904 

274.2 

50 

0.3555424 

281.5 

80     o 

0.3295663 

88     o 

0.3424646 

96     o 

0.3558239 

[68] 


TABLE  XIII.  —  CONTINUED. 

Logarithm  of  the  Elliptical  Radius  Vector. 

Argument  :     The  True  Anomaly,  v. 

0 

O 

a 

V. 

V. 

M 

V. 

w 

96°  o; 

0-3558239 

oSi  f\ 

104°  o' 

0.3694030 

oQI    / 

112°    0' 

0.3829324 

o  —  -.    0 

10 

0.3561055 

tfOl.U 

oSr     A 

IO 

0.3696864 

20O.4 
18!  1 

10 

0.3832117 

279-J 

20 

0.3563871 

JO1  .U 

,0,    0 

20 

0.3699697 

2O-J.-J 

r»Q"3     1 

2O 

0.3834908 

279.1 

3° 

0.3566689 

ZO  1  .O 

9Q,     Q 

3° 

0.3702530 

2OO.O 
18"}   o 

30 

0.3837698 

279.0 

018  8 

40 

0.3569507 

4<J  L  .0 

281.0 

40 

0.3705362 

20o.  2 
o81  1 

40 

0.3840486 

270.0 
on'B  A 

50 

0.3572326 

282.0 

50 

0.3708195 

200.  o 
283.2 

5° 

0.3843272 

^O'O 
278.4 

97     o 

0.3575146 

ofil    T 

105     o 

0.37II027 

iQ7  o 

113     o 

0.3846056 

n->W    1 

10 

0-3577967 

£OZm  L 

oSo  i 

IO 

°-37I3859 

2oo.  2 

ofi"?     ¥ 

10 

0.3848839 

27O.O 
018   o 

20 

0.3580788 

«V4|  1 

282.3 

20 

0.3716690 

2c5o.  I 
oftl  I 

20 

0.3851621 

270*2 
278.O 

30 

0.3583611 

282.3 

30 

0.3719521 

7uwt  1 

r,0-}   n 

30 

0.3854401 

40 

0.3586434 

282.4 

40 

0.3722351 

20pJ*U 

•>«•}  n 

40 

0.3857178 

277.7 
9T7   f^ 

5° 

0.3589258 

282.4 

50 

0.3725181 

^oo.u 
283.0 

50 

•0.3859954 

271.0 

277.5 

98     o 

0.3592082 

282.5 

1  06     o 

0.3728011 

114    o 

0.3862729 

II'* 

O-I1    3 

10 

°-3  5949°7 

282.6 

10 

0.3730840 

2o2>9 
282.8 

10 

0.3865502 

277.3 

20 

30 
40 

50 

0-3597733 
0.3600560 
0.3603387 
0.3606215 

282.7 
282.7 
282.8 
282.8 

20 
30 
40 

50 

0.3733668 
0.3736496 

0-3739323 
0.3742150 

282.8 
282.7 
282.7 
282.6 

20 

30 
40 

50 

0.3868272 
0.3871041 

0.3873808 
0.3876573 

277.0 
276.9 
276.7 
276.5 
276.3 

99     o 

IO 

20 

0.3609043 
0.3611872 
0.3614701 

282.9 

282.9 

282.9 

107     o 

IO 

20 

0.3744976 
0.3747801 
0.3750626 

282.5 
282.5 
282.4 

115     o 

IO 

20 

0.3879336 

0.3882097 

0.3884856 

276.1 
275.9 
O"r1  T 

30 
40 

50 

0.3617530 
0.3620360 
0.3623191 

283.0 

283.1 

283.x 

30 
40 

50 

0-3753450 
0.3756273 
0.3759095 

282.3 
282.2 
282.2 

30 
40 

50 

0.3887613 

0.3890368 
0.3893121 

270.7 
275.5 
275.3 
275.1 

IOO       O 
10 
20 
30 

0.3626022 
0.3628853 
0.3631685 
°-36345I7 

283.1 

283.2 
283.2 

283.3 

108     o 

IO 

20 
30 

0.3761917 
0.3764738 
0.3767558 
0-3770377 

282.1 
282.0 
281.9 
28l.8 

116     o 

10 

20 
30 

0.3895872 

0.3898621 
0.3901367 
0.3904111 

274.9 
274.6 
274.4 

O1/    O 

40 
50 

0.3637350 
0.3640183 

283.3 
283.3 

40 
50 

0.3773195 
0.3776012 

281.7 

28l.6 

40 
50 

0.3906853 

0-3909593 

^74.  * 

274.0 

OT^    T 

IOI       0 
IO 

0.3643016 
0-364  5849 

283.3 
283.4 

109     o 

10 

0.3778828 
0.3781643 

281.5 
28l.5 

117     o 

10 

0.3912330 
0.3915065 

•*70>7 
273.5 
273.3 

20 

0.3648683 

283.4 

20 

0.3784458 

281.3 

20 

0.3917798 

273.0 

3° 

0.3651517 

283.4 

30 

0.3787271 

28l.2 

30 

0.3920528 

272.8 

40 

5° 

0-3654351 
0.3657185 

283.4 
283.4 

40 
50 

0.3790083 
0.3792894 

28I.J 
28l.O 

4°. 

50 

0.3923256 
0.3925981 

272.5 

OTT    ^ 

IO2      0 

0^3660019 

283.4 

110       0 

0.3795704 

280.8 

118     o 

0.3928704 

Z  1  4.  J 

910  n 

IO 

0.3662853 

283.4 

10 

0.3798512 

280.8 

10 

0.3931424 

*  /  *>w 
271.8 

2O 

3° 
40 

5° 

0.3665687 
0.3668522 
0.3671357 
0.3674191 

283.5 
283.5 
283.4 
283.5 

20 

30 
40 

5° 

0.3801320 
0.3804126 
0.3806932 
0.3809736 

280.6 
280.6 
280.4 
280.2 

20 

3° 
40 

50 

0.3934142 
0.3936857 

0-393957° 
0.3942280 

271.5 
271.3 
271.0 
270.8 

103     o 

0.3677026 

283.4 

III       0 

0.3812538 

28c.I 

119     o 

0.3944988 

Oln  K 

10 

20 

30 
40 

50 

0.3679860 
0.3682695 
0.3685529 
0.3688363 
0.3691196 

283.5 
283.4 
283.4 
283.3 

283.4 

10 
20 
30 

4° 
5° 

o-38i5339 
0.3818139 
0.3820937 
0.3823734 
0.3826530 

28o.O 
279.8 
279.7 
279.6 
2TO  / 

10 

20 
30 
40 

50 

0-3947693 
0-3950395 
0-3953094 
o-395579i 
0.3958485 

2  jiJ.  J 
270.2 
269.9         ' 
269.7 
269.4 

104     o 

0.3694030 

112       0 

0.3829324 

•fir* 

1  2O       0 

0.3961176 

269.1 

[69] 


TABLE  XIII.—  CONTINUED. 

Logarithm  of  the  Elliptical  Radius  Vector. 

V. 

120°     0' 
IO 

0.3961176 
0.3963864 

d 

M 

268.8 

V. 
128°  o' 

10 

0.4086450 
0.4088967 

d 

251.7 

V. 

136°  o' 

10 

0.4201901 
0.4204178 

6 

227.7 

20 
3° 

0.3966549 
0.3969231 

268.2 

oA&  n. 

20 

30 

0.4091479 

0.4093987 

sSi.3 

25o.8 

20 
30 

0.4206450 
0.4208716 

227.2 
226.6 

.! 

40 
So 

0.3971911 
0,3974588 

JOO.O 

267.7 

40 
50 

0.4096491 
0.4098990 

249-9 

40 

5° 

0.4210977 
0.4213231 

226.  1 

225.4 

121       O 

0.3977261 

267.3 
267.0 

129     o 

0.4101485 

249.5 
249.0 

137     o 

0.4215480 

224.9 

224.3 

IO 

0.3979931 

o  A/I  8 

IO 

0.4103975 

10 

0.4217723 

nnl     Q 

20 
30 

0.3982599 

0.3985263 

2OO.O 
266.4 

20 

3° 

0.4106461 

0.4108943 

248.2 

9  /.I    n 

20 
.    30 

0.4219961 
0.4222192 

223.  0 
223.1 

n  n  n     & 

40 

0.3987924 

2      •* 

40 

0.4111420 

247.7 

40 

0.4224417 

222.3 

50 

0.39905,82 

/•  e    c 

50 

0.4113893 

_  ff     Q 

5° 

0.4226636 

221.9 

2OD.O 

240.8 

221.3 

122       O 

0.3993237 

130     o 

0.4116361 

246.3 

138     o 

0.4228849 

10 

0.3995889 

2    '2 

10 

0.41  18824 

10 

0.4231056 

220.7 

2O 

0.3998537 

V's 

20 

0.4121283 

9X1  / 

20 

0.4233257 

220.  1 

30 
40 

50 

0.4001  182 
0.4003824 
0.4006463 

264.2 
263.9 
263.5 

30 
40 

5° 

o-4I23737 
0.41  26186 
0.4128630 

44*J.£l 
244-9 
244-4 
244.0 

30 
40 

50 

0.4235452 
0.4237641 

0.4239824 

219.5 

218.9 
218.3 

217.6 

123     o 

0.4009098 

263.2 

131     o 

0.4131070 

243.5 

139     o 

0.4242000 

•  •  f»V 

2  17.0 

IO 

0.401  1730 

262.8 

10 

0.4133505 

243.O 

10 

0.4244170 

2O 

0.4014358 

262.5 

20 

0.4135935 

242.5 

20 

0.4246335 

n  t  K    O 

30 

0.4016983 

262  2 

3° 

0.4138360 

242.1 

30 

0.4248493 

2  1  J.O 

40 

0.4019605 

261.8 

40 

0.4140781 

241.5 

40 

0.4250644 

21  5.  J 
214.6 

50 

0.4022223 

261.4 

5° 

0.4143196 

24I.I 

50 

0.4252790 

2  1  3.Q 

124     o 

0.4024837 

261  *  I 

132     o 

0.4145607 

240.5 

140     o 

0.4254929 

2  1  3.  2 

10 

0.4027448 

260.7 

10 

0.4148012 

240.1 

10 

0.4257061 

212.6 

20 

0.4030055 

260  /I 

20 

0.4150413 

239.5 

20 

0.4259187 

30 

0.4032659 

260.0 

3° 

0.4152808 

239.1 

30 

0.4261307 

21  2.O 
211.  4 

40 

0.4035259 

25o.6 

40 

0.4155199 

238.5 

40 

0.4263421 

50 

0.4037855 

25o.3 

50 

0.4157584 

238.1 

50 

0.4265528 

210.7 
210.  1 

125     o 

10 

20 

0.4040448 

0.4043037 

0.4045622 

fcvv 

258.9 
258.5 
258.1 

133     o 

IO 
20 

0.4159965 
0.4162340 
0.4164710 

237.5 
237.0 
236.5 

141     o 

IO 
20 

0.4267629 

0.4269723 

0.4271811 

209.4 
208.8 

30 

0.4048203 

257.8 

3° 

0.4167075 

236.O 

30 

0.4273892 

20    .1 

40 

0.4050781 

257.4 

40 

0.4169435 

'  235.4 

40 

0.4275966 

207.4 
206.8 

50 

0.4053355 

•**•'  /•** 
257.0 

5° 

0.4171789 

234.9 

5° 

0.4278034 

2o6.  1 

126     o 

10 

0.4055925 

0.4058491 

256.6 

256.  2 

134     o 

IO 

0.4174138 
0.4176482 

234-4 
233.8 

142     o 

10 

0.4280095 
0.428^149 

2o5.4 

20 

0.4061053 

255.8 

20 

0.4178820 

233.3 

20 

0.4284197 

20  /  ¥ 

30 

0.406361  1 

255.4 

30 

0.4181153 

232.7 

30 

0.4286238 

2o3.4 

40 

0.4066165 

255.0 

40 

0.4183480 

/ 

232.2 

40 

0.4288272 

2O2.  7 

50 

0.4068715 

254.6 

50 

0.4185802 

23i.6 

50 

0.4290299 

2O2.I 

127     o 

0.4071261 

254.2 

135     o 

0.4188118 

23l.I 

H3     o 

0.4292320 

201.3 

10 

0.4073803 

253.8 

10 

0.4190429 

23o.6 

10 

0.4294333 

2OO.7 

20 

0.4076341 

253.3 

20 

0.4192735 

93r>  n 

20 

0.4296340 

/ 
20O.O 

30 

0.4078874 

253.  o 

30 

0-4195035       229.4 

30 

0.4298340 

199.3 

40 

0.4081404 

252.5 

40 

0.4197329       22g 

40 

0.4300333 

198.6 

50 

0.4083929 

252.1 

50 

0.4.100618   i 

22  8  3 

50 

0.4302319 

7 

197.9 

128     o 

0.4086450 

136     o 

0.4201901   ' 

144     o 

0.4304298 

[70] 


TABLE  XIIL—  CONTINUED. 

Logarithm  of  the  Elliptical  Radius  Vector. 

V. 

144°   o' 

0.4304298 

IQ1    1 

V. 

152°   o' 

0.4390569 

160.6 

V. 
I  60°    0' 

0.4457969 

O 

T1Q  A 

10 

0.4306270 

*V  r* 

IO 

0.4392175 

T  ^n  T 

IO 

0.4459155 

1  I  O.U 

20 

0.4308235 

lr.K  Q 

20 

0.4393772 

1  J9-  7 

20 

o.446°332 

117.7 

*  t  A   O 

3° 

0.4310193 

1  Cy  J.  O 

30 

0-4395361 

i58.o 

30 

0.4461500 

IIO.O 
_  _  e   Q 

40 

0.4312144 

i\ 

40 

0.4396941 

40 

0.4462658 

113.  0 
_  _  jr    _ 

5° 

0.4314088 

194'4 

io3.6 

5° 

0-43975  H 

156.4 

50 

0.4463808 

113.  O 

145     o 

0.4316024 

*  7 

io3.o 

153     o 

0.4400078 

i55.6 

161     o 

0.4464948 

n3.i 

IO 

o-43I7954 

IQ2  2 

10 

0.4401634 

10 

0.4466079 

20 

0.4319876 

191.5 

20 

0.4403181 

i53.9 

20 

0.4467201 

112.2 
III.  2 

3° 

0.4321791 

loo  8 

30 

0.4404720 

i53.i 

3° 

0.4468313 

40 

0.4323699 

loo.  i 

40 

0.4406251 

l52.2 

40 

0.4469416 

IIO.O 

50 

0.4325600 

189.3 

50 

0.4407773 

i5i.4 

50 

0.4470510 

I09.4 
108.4 

146     o 

0.4327493 

188.6 

154     o 

0.4409287 

i5o.5 

162     o 

0-447  *  594 

107.5 

10 

0.4329379 

187.8 

10 

0.4410792 

lAo.l 

10 

0.4472669 

1  06.  5 

20 

o.433I257 

187.1 

20 

0.4412289 

4v  / 
148.8 

20 

0.4473734 

io5.6 

3° 

o-4333I28 

/ 

186.3 

3° 

0.4413777 

148.0 

-    30 

0-447479° 

104.7 

40 

0-43  3499  * 

i85.6 

40 

0.4415257 

40 

0.4475837 

io3  i 

5° 

0.4336847 

184.9 

5° 

0.4416728 

146.2 

50 

0.4476874 

i\j*j.  i 
102.7 

147     o 

0.4338696 

184.1 

155     o 

0.4418190 

145.4 

163     o 

0.4477901 

101.8 

IO 

0.4340537 

i83.4 

IO 

0.4419644 

144-5 

10 

0.4478919 

IOQ.8 

20 

0.4342371 

182.6 

20 

0.4421089 

143.6 

20 

0.4479927 

99.9 

30 

o.4344'97 

181.9 

3° 

0.4422525 

142.8 

30 

0.4480926 

08.0 

40 

0.4346016 

40 

0.4423953 

141.0 

4° 

0.4481915 

Vv  V 

98.0 

5° 

04347827 

180.4 

50 

0.4425372 

•**•  »y 
14i.  i 

50 

0.4482895 

7. 

97.0 

148     o 

0.4349631 

170.6 

156     o 

0.4426783 

i4o.i 

164     o 

0.4483865 

06.  1 

10 

0.4351427 

17 
178.8 

10 

0,4428184 

139.3 

10 

0.4484826 

7 

95.i 

20 

0.4353215 

178.0 

20 

0.4429577 

i38.4 

20 

0.4485777 

94.  i 

30 

0-4354995 

177.3 

30 

0.4430961 

i37.6 

30 

0.4486718 

o3  2 

40 

0.4356768 

*  /  /-v 
176.5 

40 

0.4432337 

BkT  J*W 

i36.6 

40 

0.4487650 

y*-'.* 
02.  2 

50 

0.4358533 

175.8 

50 

0-443  3  7°3 

135.8 

50 

0.4488572 

7 
91.3 

149     o 

0.4360291 

174.  Q 

157     o 

0.4435061 

165  .  o 

0.4489485 

QO.  3 

10 

0.4362040 

/^**y 
174.2 

10 

0.4436410 

i34.o 

IO 

0.4490388 

80.3 

20 

0.4363782 

*   /*+•  * 

n3.4 

20 

0-443775° 

i33.i 

20 

0.4491281 

wvftv 

88.4 

30 

0.4365516 

1    /x^.if 
172.6 

30 

0.4439081 

l32.3 

3° 

0,4492165 

87.4 

40 

0.4367242 

I7I.8 

40 

0.4440404 

i3i.3 

40 

0.4493039 

86.4 

5° 

0.4368960 

17I.I 

50 

0-4441  71  7 

i3o.5 

50 

0.4493903 

85.5 

150     o 

0.4370671 

I7O.2 

158     o 

0.4443022 

129.5 

1  66     o 

0.4494758 

IO 

0.4372373 

10 

°-44443I7 

128.7 

10 

0.4495602 

83.5 

20 

0.4374068 

168.6 

20 

0.4445604 

20 

0.4496437 

82.5 

3° 

0-4375754 

167.8 

3° 

0.4446881 

126.8 

3° 

0.4497262 

81.6 

40 

0.4377432 

I67.O 

40 

0.4448149 

125.9 

40 

0.4498078 

8o.5 

50 

0.4379102 

166.3 

50 

0.4449408 

I25.I 

50 

0.4498883 

7O.6 

151      o 

0.4380765 

i65.4 

159     o 

0.445065-9 

124.1 

167     o 

0.4499679 

/y*v 
78.6 

10 

0.4382419 

164.6 

10 

0.4451900 

123.2 

10 

0.4500465 

T7   A 

20 

0.4384065 

i63.8 

20 

o-445  3  i  32 

122.3 

20 

0.4501241 

77.O 
76.6 

3° 

0-4385703 

i63.o 

30 

°-4454355 

I2I.4 

3° 

0.4502007 

1*1    1 

40 

0-4387333 

162.2 

40 

°-4455569 

120.4 

40 

0.4502764 

7J-7 

5° 

0.4388955 

161.4 

50 

0.4456773 

119.6 

50 

0.4503510 

73.7 

152     o 

0.4390569 

1  60     o 

0.4457969 

168     o      0.4504247 

[71] 


TABLE  XIII.—  CONCLUDED. 

Logarithm  of  the  Elliptical  Radius  Vector. 

Argument  :  The  True  Anomaly,  v. 

O 

o 

O 

V. 

M 

V. 

r. 

V. 

M 

1  68°  o' 

10 
20 

30 
40 

50 

0.4504247 
0.4504973 
0.4505690 
0.4506397 
0.4507094 
0.4507781 

72.6 
71.7 
70.7 
69.7 
68.7 

172°  o' 

IO 

20 

30 
40 

50 

0.4518935 
0.4519421 

0.4519898 

0.4520364 

0.4520820 
0.4521266 

48.6 

47.7 

46.6 
45.6 
44.6 
ft  f. 

176°  o' 

10 

20 

30 
40 

50 

0.4527802 
0.4528043 
0.4528275 
0.4528496 
0.4528707 
0.4528908- 

24.1 

23.2 
22.1 
21.  1 
20.1 

169  o 

0.4508458 

66  7 

173  o 

0.4521702 

42  5 

177  o 

0.4529098 

18  o 

10 

20 

3° 
40 

0.4509125 
0.4509782 
0.4510430 
0.4511067 

65.7 
64.8 
63.7 

10 

20 

30 
40 

0.4522127 

0.4522543 

0.4522948 

0.4523343 

41.6 
4o.5 
39.5 
38  5 

IO 
20 
30 
40 

0.4529278 
0.4529448 
0.4529607 
0.4529756 

17-0 
1  5.9 
14.9 

50 

0.4511694 

61.7 

50 

0.4523728 

37.5 

50 

0.4529895 

12.9 

170  o 

IO 
20 
30 
40 

50 

171  o 

10 

20 

30 

0.4512311 
0.4512918 

0-45  i  35  '5 
0.4514102 

0.4514680 
0.4515247 

0.4515804 
0.4516351 
0.4516888 
0.4517415 

60.7 
59.7 
58.7 
57.7 
56.7 
55.7 

54-7 
53.7 
52.7 
5i  7 

174  o 

IO 

20 

30 
40 

50 

175  o 

10 

20 

30 

0.4524103 

0.4524468 
0.4524822 
0.4525166 

0.4525499 
0.4525823 

0.4526136 
0.4526440 

0.4526733 

0.4527016 

36.5 
35.4 
34-4 
33.3 
32.4 
3i.3 

3o.4 
29.3 
28.3 

2T  3 

178  o 

10 
20 
30 
40 
50 

179  o 

IO 

20 

30 

0.4530024 
0.4530142 
0.4530250 

0.4530348 
0.4530436 

0.4530513 
0.4530580 

0.4530637 
0.4530683 
0.4530719 

11.  8 
10.8 

9.8 
8.8 
7-7 
6.7 
5.7 
4.6 
3.6 
3  6 

40 

0.4517932 

5o  6 

40 

0.4527288 

4° 

0.4530745 

50 

0.4518438 

49-7 

50 

0.4527550 

25.2 

50 

0.4530761 

o  5 

172  o 

0.4518935 

176  o 

0.4527802 

1  80  o 

0.4530766 

If  v  is  greater  than  180°,  take  180°  —  v  as  Argument. 

172  I 


TABLE  XIV. 

Auxiliary  Quantities,  for  Computation  of  the  Heliocentric  Co-ordinates. 

(Referred  to  the  Equator,  and  to  the  Mean  Equinox  at  the  beginning  of  the  Year.) 

Year. 

A 

B. 

C. 

Log.  a. 

Log.  b. 

Log.  c. 

1850 

3I°2l'  l8".20 

299°  i  '26^.50 

32o°55'  52^.99 

9.9968336 

9.9768259 

9.5316651 

1851 

31  22   8  .59 

299  2  14  .66 

320  56  48  .05 

9.9968326 

9.9768218 

9.5317063 

1852  B 

31  22  59  .12 

299  3  2  .96 

320  57  43  .27 

9.9968315 

9.9768177 

9.53I7477 

1853 

31  23  49  -5  * 

299  3  5i  .12 

320  58  38  .33 

9.9968304 

9.9768136 

9.5317889 

1854 

31  24  39  -89 

299  4  39  .29 

320  59  33  .39 

9.9968294 

9.9768094 

9.5318302 

1855 

31  25  30  .28 

299  5  27  .45 

321  o  28  .45 

9.9968283 

9.9768053 

9-5318714 

1856  B 

31  26  20  .81 

299  6  15  .75 

321  i  23  .64 

9.9968272 

9.9768011 

9.5319128 

1857 

31  27  II  .20 

299  7  3  -91 

321  2  18  .68 

9.9968261 

9-9767970 

9.531954° 

1858 

31  28   I  .58 

299  7  52  .08 

321  3  13  .72 

9.9968251 

9.9767928 

9.53I9953 

1859 

31  28  5'  -97 

299  8  40  .24 

321  4  8  .75 

9.9968240 

9.9767887 

9.5320365 

1860  B 

31  29  42  .50 

299  9  28  .54 

321  5  3  .92 

9.9968229 

9.9767846 

9.5320778 

1861 

31  30  32  .89 

299  10  16  .71 

321  5  58  .94 

9.9968218 

9-9767805 

9.5321190 

1862 

31  31  23  .29 

299  ii  4  .88 

321  6  53  .95 

9.9968208 

9.9767763 

9.5321603 

1863 

31  32  13  .68 

299  ii  53  -05 

321  7  48  .96 

9.9968197 

9.9767722 

9-5322015 

1864^' 

3^  33  4-2i 

299  12  41  .35 

321  8  44  .  1  1 

9.9968186 

9.9767680 

9.5322428 

1865 

3»  33  54  -61 

299  '3  29  -53 

321  9  39  .10 

9.9968175 

9.9767639 

9.5322840 

1866 

3»  34  45  -OI 

299  H  17  -7° 

321  10  34  .09 

9.9968165 

9.9767597 

9-5323253 

1867 

31  35  35  -41 

299  15  5  .87 

321  ii  29  .08 

9.9968154 

9.9767556 

9-5323665 

1868  B 

3i  36  25  .95 

299  15  54.18 

321  12  24  .20 

9.9968143 

9.9767514 

9.5324078 

1869 

31  37  16.35 

299  16  42  .36 

321  13  19  .17 

9.9968132 

9-9767473 

9.5324490 

1870 

31  38  6.75 

299  17  30-53 

321  14  14.14 

9.9968122 

9.9767431 

9.5324903 

1871 

31  38  57  -16 

299  1  8  1  8  .71 

321  15  9  .10 

9.99681  ii 

9.9767390 

9-5325315 

1872  B 

31  39  47  -7° 

299  19  7  .02 

321  16  4  .20 

9.9968100 

9.9767348 

9.5325728 

1873 

31  40  38  .10 

299  19  55  .20 

321  16  59  .14 

9.9968089 

9.9767306 

9.5326140 

1874 

31  41  28  .50 

299  20  43  .37 

321  17  54.08 

9.9968079 

9.9767265 

9.5326552 

1875 

31  42  1  8  .91 

299  21  31  .55 

321  1  8  49  .02 

9.9968068 

9.9767223 

9.5326964 

1876-6 

3i  43  9-45 

299  22  19  .86 

321  19  44  .10 

9.9968057 

9.9767181 

9-5327377 

1877 

31  43  59  -86 

299  23  8  .04 

321  20  39  .02 

9.9968046 

9.9767140 

9.5327789 

1878 

31  44  50.26 

299  23  56  .22 

321  21  33  .93 

9.9968036 

9.9767098 

9.5328201 

1879 

31  45  40.67 

299  24  44  .40 

321  22  28  .84 

9.9968025 

9.9767057 

9.5328613 

1880  B 

31  46  31  .21 

299  25  32  .71 

321  23  23  .89 

9.9968014 

9.9767015 

9.5329026 

1881 

31  47  21  .62 

299  26  20  .90 

321  24  18  .78 

9.9968003 

9.9766973 

9-5329437 

1882 

31  48  12  .02 

299  27  9  .08 

321  25  13  .67 

9.9967993 

9.9766932 

9.5329849 

1883 

3  1  49  -  2  .43 

299  27  57  .27 

321  26  8  .56 

9.9967982 

9.9766890 

9.5330261 

1884  /.' 

3i  49  5Z  -98 

299  28  45  .58 

321  27  3  .58 

9.9967971 

9.9766848 

9.5330674 

1885 

31  50  43  .38 

299  29  33  .77 

321  27  58  .45 

9.9967960 

9.9766806 

9.5331085 

1886 

31  51  33  -79 

299  30  21  .95 

321  28  53  .32 

9.9967950 

9.9766765 

9-533H97 

1887 

3152  24  .20 

299  31  10  .14 

321  29  48  .18 

9.9967939 

9.9766723 

9-533I909 

1888  B 

3*  53  H-75 

299  31  58  .46 

321  30  43  .18 

9.9967928 

9.9766081 

9.5332322 

1889 

3i  54  5  -15 

299  32  46  -65 

321  31  38  .03 

9.9967917 

9.9766639 

9-5332733 

1890 

3i  54  55  -56 

299  33  34  -83 

321  32  32  .87 

9.9967907 

9.9766598 

9-5333H5 

1891 

3i  55  45  -97 

299  34  23  .02 

321  33  27  .72 

9.9967896 

9.9766556 

9-5333557 

1892  B 

31  56  36.52 

299  35  ii  -34 

321  34  22  .70 

9.9967885   9.9766514 

9-5333970 

1893 

31  57  26  .93 

299  35  59  -53 

321  35  17  -53 

9.9967874  9.9766472 

9-533438i 

1894 

3i  S8  17  -34 

299  36  47  .72 

321  36  12  .35 

9.9967864  9.9766430 

9-5334793 

1895 

3i  59  7  -75 

299  37  35  -91 

321  37  7  -17 

9-9967853   9-9766388 

9-5335205 

1896  B 

31  59  58  .30 

299  38  24  .23 

321  38   2  .13 

9.9967842   9.9766346 

9.5335618 

1897 

32  o  48  .71 

299  39  I2  .42 

321  38  56.93 

9.9967831   9.9766304 

9.5336029 

1898 

32  i  39  .12 

299  40  o  .61 

321  39  5i  -73 

9.9967821 

9.9766263 

9-5336441 

1899 

32   2  29  .54 

299  40  48  .81 

321  40  46  .52 

9.9967810 

9.9766221 

9-5336852 

1900 

32  3  '9  -96 

299  41  37  .00 

321  41  4»  -32 

9-9967799 

9.9766179 

9-5337264 

[73] 


TABLE  XV. 

To  find  the  Corrections  of  the  three  Co-ordinates  a?,  y,  z  from  %. 

A  X.                     A  y.                  A  z. 

I' 

1850. 

1900. 

1850. 

1900. 

1850. 

1900. 

—  5000 

+  7237 

+  7296 

+  19136 

+  19217 

—  56560 

-56525 

4900 

7117 

7175 

18818 

18897 

55620 

55585 

4800 

6996 

7053 

18500 

18578 

54679 

54645 

1      i 

4700 

6876 

6932 

18181 

18258 

53739 

53705 

1  20. 

122. 

4600 

6756 

6811 

17863 

17939 

52799 

52766 

4500 

6635 

6689 

17545 

17619 

51858 

51826 

i 

i 

I 

4400 

6515 

6568 

17227 

17300 

50918 

50886 

2 

2 

2 

4300 

6395 

6447 

16909 

16980 

49978 

49946 

3 

4 

4 

4200 

6275 

6326 

16590 

16661 

49038 

49007 

4 

5 

5 

4100 

6154 

6204 

16272 

16341 

48097 

48067 

5 

6 

6 

—4000 

+  6034 

+  6083 

+  15954 

+  16022 

-47157 

-47127 

6 

7 

7 

3900 

59H 

5962 

15636 

15702 

46217 

46187 

7 

8 

8 

3800 

5793 

5840 

I53i8 

15383 

45276 

45247 

8 

10 

10 

3700 

5673 

5719 

15000 

15063 

44336 

44308 

9 

1  1 

ii 

3600 

5552 

5598 

14682 

14744 

43395 

43368 

10 

12 

12 

3500 

5432 

5476 

H363 

14424 

42455 

42428 

20 

24 

£ 

24 

3400 

S312- 

5355 

14045 

14105 

415*5 

41488 

30 

36 

37 

3300 

5191 

5234 

13727 

13785 

4°574 

40549 

40 

48 

> 

49 

3200 

5071 

5"3 

J3409 

13466 

39634 

39609 

50 

6O 

61 

3100 

495° 

4991 

13091 

13146 

38693 

38669 

60 

72 

73 

—3000 

+  4830 

+  4870 

+  12773 

+  12827 

-37753 

-37729 

70 

O 

84 

S 

85 

2900 

4710 

4749 

12455 

12507 

36813 

36789 

8°. 

96 

_   o 

98 

2800 

4589 

4627 

12137 

12188 

35872 

35849 

90' 

108 

I  IO 

2700 

4469 

4506 

11818 

11868 

34932 

349  10 

2600 

4349 

4385 

11500 

11549 

33991 

3397° 

2500 

4228 

4263 

11182 

1  1229 

33051 

33030 

2400 

4108 

4142 

10864 

10910 

3211  1 

32090 

318. 

320. 

2300 

3988 

4021 

10546 

10590 

31170 

31150 

22OO 

3868 

3900 

10227 

10271 

30230 

3021  1 

i 

3 

3 

2100 

3747 

3778 

9909 

995  i 

29289 

29271 

2 

6 

—  2OOO 

+  3627 

+  3657 

+  959* 

+  9632 

-28349 

-28331 

3 

10 

IO 

1900 

3507 

3536 

9273 

9312 

27409 

27391 

4 

13 

_  s 

13 

.  £. 

l8oo 

3386 

34*4 

8955 

8993 

26468 

26452 

5 

10 

IO 

1700 

3266 

3293 

8637 

8673 

25528 

25512 

19 

19 

1600 

3H6 

3I71 

8319 

8354 

24588 

24572 

7 

22 

22 

s 

1500 

3025 

3050 

8000 

8034 

23647 

23632 

8 

25 

20 

I40O 

2905 

2927 

7682 

7715 

22707 

22693 

9 

29 

29 

1300 

27J5 

2807 

7364 

7395 

21767 

21753 

10 

32 

S 

3Z 
s 

I20O 

2665 

2686 

7046 

7076 

20827 

20813 

20 

64 

64 

I  I  00 

2544 

2564 

6728 

6756 

19886 

19874 

30 

95 

96 

o 

|  IOOO 

+  2424 

+  2443 

+  6410 

+  6437 

-18945 

-18934 

40 

127 

120 
.  £.~ 

900 

2304 

2322 

6092 

6117 

18005 

17994 

5° 

s 

!59 

I  DO 

800 

2183 

22OO 

5774 

5798 

17064 

17054 

DO 

191 

192 

700 

2063 

2079 

5455 

5478 

16124 

16115 

70 

O^*. 

223 

224 

600 

1942 

I958 

5*37 

5'59 

15184 

15175 

oo 

254 

r\  s 

256 

500 

1822 

1836 

4819 

4839 

H243 

H235 

90 

286 

288 

400 

1702 

1715 

4501 

4520 

i3303 

i3295 

300 

1581 

'594 

4183 

4200 

12363 

12355 

20O 

1461 

H73 

3864 

3881 

11423 

1  1416 

100 

»34° 

I351 

3546 

3561 

10482 

10476 

O 

+  1220 

+  1230 

+  3228 

+  3242 

-  9542 

-  9536 

[74] 


TABLE  XV.—  CON'CLUDED. 

To  find  the  Corrections  of  the  three  Co-ordinates  a?,  y,  z  from 

e 

Ax.                   Ay.                Az. 

c- 

1850. 

1900. 

1850. 

1900. 

1850. 

1900. 

o 

+  I22O 

+  1230 

+  3228 

+  3242 

-  9542 

-  9536 

+  100 

I  1  00 

1109 

2910 

2922 

8602 

8596 

2OO 

979 

987 

2592 

2603 

7661 

7656 

3OO 

859 

866 

2274 

2283 

6721 

6717 

400 

739 

745 

1956 

1964 

5780 

5777 

500 

618 

624 

1637 

1644 

4840 

4837 

600 

498 

502 

1319 

1325 

3900 

3897 

7OO 

378 

381 

1  00  1 

1005 

2959 

2957 

800 

258 

260 

683 

686 

2019 

2018 

9OO 

+  138 

+  138 

+   365 

+  366 

—  1078 

—  1078 

+  1000 

+  -  17 

+   17 

+   47 

+   47 

-  138 

138 

939- 

941. 

I  TOO 

—  104 

—  104 

—  271 

—  .  272 

+  802 

+  802 

1200 

224 

226 

589 

592 

1743 

1742 

i 

9 

9 

1300 

344 

347 

907 

911 

2683 

2681 

2 

19 

—  O 

19 

Q 

1400 

464 

468 

1225 

1231 

3624 

3621 

3 

28 

20 

1500 

584 

589 

J543 

1550 

4564 

4561 

4 

37 

38 

l6oO 

705 

711 

1862 

1870 

55°4 

5501 

5 

47 

s- 

47 

1700 

825 

832 

2180 

2189 

6445 

6441 

6 

56 

£  £ 

56 

£1  £ 

1800 

945 

95.3 

2498 

2509 

7385 

738o 

7 

66 

66 

1900 

1066 

1075 

2816 

2828 

8326 

8320 

8 

75 

o  - 

75 

+  2000 

—  1186 

—  1196 

-  3^34 

-  3H8 

+  9266 

+  9260 

9 

85 

85 

2100 

1306 

1317 

3452 

3467 

10206 

IO2OO 

TO 

94 

o  o 

94 

*  O  Q 

2200 

1427 

H39 

3770 

3787 

11147 

III4O 

20 

188 

f\ 

188 

2300 

1547 

1560 

4089 

4107 

12087 

12079 

30 

282 

_s 

282 

s 

2400 

1668 

1681 

4407 

4426 

13027 

13019 

40 

376 

s 

376 

2500 

1788 

1802 

4725 

4745 

13967 

*3959 

5° 

s 

469 

_  s 

470 

-  £  - 

2600 

1908 

1924 

5043 

5065 

14908 

14899 

60 

563 

£  -  — 

565 

£  - 

2700 

2029 

2045 

5361 

5384 

15848 

15839 

70 

657 

659 

2800 

2149 

2166 

5680 

57°4 

16788 

16778 

80 

75i 

753 

2900 

2270 

2288 

5998 

6023 

17729 

17718 

90 

845 

847 

+  30OO 

-2390 

—  2409 

—  6316 

-  6343 

+  18669 

+  18658 

3100 

2510 

2530 

6634 

6662 

19610 

19598 

3200 

2631 

2652 

6952 

6982 

20551 

20537 

33°° 

2751 

2773 

7270 

7301 

21491 

2H77 

3400 

2871 

2895 

7588 

7621 

22431 

22417 

3500 

2991 

3016 

7906 

7940 

23371 

23356 

3600 

3112 

3J37 

8225 

8260 

24312 

24296 

3700 

3232 

3259 

8543 

8579 

25252 

25236 

3800 

3352 

338o 

8861 

8899 

26192 

26176 

3900 

3473 

3502 

9179 

9218 

27133 

27115 

+  4000 

-3593 

-3623 

-  9497 

-  9538 

+  28073 

+  28055 

4100  - 

3713 

3744 

9815 

9857 

29013 

28995 

4200 

3834 

3866 

10133 

10177 

29954 

29935 

4300 

3954 

3987 

10452 

10496 

30994 

30874 

4400 

4074 

4108 

10770 

10816 

31835 

31814 

4500 

4194 

4229 

11088 

11135 

32775 

32754 

4600 

43  i  5 

435  i 

11406 

"455 

33715 

33694 

4700 

4435 

4472 

11724 

11774 

34656 

34634 

4800 

4555 

4593 

12043 

12094 

35596 

35573 

4900 

4676 

4715 

12361 

12413 

36537 

36513 

+  5000   —  4796 

—4836   —12679 

-12733 

+  37477   +37454 

[75] 


TABLE  XVI. 

To  be  used  for  Calculating  an  Approximate  Place, 

When  only  the  first  five  Equations  are  taken  into  account. 


f. 

AJB. 

Ay. 

Ag. 

—  5000 

+  70 

+  184 

-543 

—4000 

57 

152 

449 

—  3000 

45 

1  20 

355 

—  2OOO 

33 

88 

261 

—  IOOO 

21 

56 

167 

O 

+  9 

+  25 

-  73 

+  1000 

-  3 

-  7 

+  21 

2OOO 

H 

39 

"5 

3OOO 

27 

7i 

209 

4OOO 

39 

103 

303 

50OO 

-5^ 

-134 

+  397 

(Units  of  the  fifth  decimal.) 


[76] 


TABLE  XVII. 

To  be  used  for  Calculating  an  Approximate  Place 

When  only  the  First  Five  Equations  are  taken  into  account. 

M. 

V. 

Log.  r. 

V. 

V. 

Log.  r. 

V. 

V. 

Log.  r. 

V. 

V. 

Log.  r. 

5 

1850 

324°49'  5"-9 

0° 

0.25992 

"360° 

45° 

0.28339 

315° 

90° 

0-3459° 

270 

135° 

0.41894 

22 

1851 

65  41  o  .° 

i 

0-25994359 

46  0.28442 

3H 

91 

0.34756 

269 

136 

0.42032 

22 

1852  L 

1  66  49  30  .! 

2 

0.25997  358 

47  0-28547 

3i3 

92 

0-34923 

268 

137 

0.42168 

22 

1853 

267  41  24  .8 

3 

0.26003 

357 

48  0.28653 

312 

93 

0.35091 

267 

138 

0.42302 

22 

1854 

8  33  19  .4 

4 

0.2601  1 

356 

49 

0.28662 

3ii 

94 

0.35259 

266 

139  jo-42433 

22 

1855 

109  25  14  .1 

5 

0.26022 

355 

5° 

0.28872 

31° 

95 

0.35427 

265 

140 

0.42562 

22 

1856  .Z?  2TO  22  Al   6 

I857 

1858 

311  25  38  .3 

C2  17  3?  .O 

6 

7 

0.26035354 
0.2605  !  353 

5i 

52 

0.28985 
0.29099 

3°9 

308 

96 
97 

0.35596 

0.35765 

264 
263 

141 
142 

0.42689  21 
0.42814121 

5 

185,9 

j    I  J  j  ' 
I  r  2   Q  27  6 

8 

0.26068 

352 

53 

0.29215 

3°7 

98 

0-35934 

262 

H3 

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[77 


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